the logarithmic sobolev inequality for discrete spin systems on a lattice for finite range lattice gases with a finite spin space it is shown that the dobrushin shlosman mixing condition is equivalent to the existence of a logarithmic sobolev inequality for the associated unique gibbs state in addition implications of these considerations for the ergodic properties of the corresponding glauber dynamics are examined

multivariate periodic arma 1 1 processes the main objective of this paper is to investigate the properties of multivariate periodic autoregressive moving average arma l 1 processes such properties include the covariance structure the parameter space and estimation the parameter space of such periodic processes is derived by aggregation for instance monthly models will aggregate to annual models in particular the parameter space and estimation are analyzed for contemporaneous arma carma models it is shown that in general the aggregation of a multivariate periodic arma 1 1 model leads to a stationary multivariate arma 1 1 model however not always a periodic carma 1 1 model aggregates into a stationary carma 1 1 model furthermore it is shown that in estimating the aggregated model parameters the method based on the periodic model and corresponding parameters is superior to that based on the aggregated series

coercive inequalities for gibbs measures abstract we prove the generalized nash and logarithmic nash inequalities for gibbs measures with dirichlet form associated to the kawasaki dynamics

poincare and transportation inequalities for gibbs measures under the dobrushin uniqueness condition in in this paper we establish an explicit and sharp estimate of the spectral gap poincare inequality and the transportation inequality for gibbs measures under the dobrushin uniqueness condition moreover we give a generalization of the liggett s m e theorem for interacting particle systems

aggregation and estimation for low order periodic arma models the aggregated time series resulting from summing over the seasons of a seasonal time series which is assumed to follow either an ar 1 or arma 1 1 model having periodic seasonal parameters is shown to follow an arma 1 1 model parameter estimation for such models is investigated analytically and via simulation significant gain in parameter estimation efficiency at the aggregated level is demonstrated when the seasonal data and their model is utilized rather than the aggregated annual data and their model

logarithmic sobolev inequalities for mollified compactly supported measures abstract we show that the convolution of a compactly supported measure on r with a gaussian measure satisfies a logarithmic sobolev inequality lsi we use this result to give a new proof of a classical result in random matrix theory that states that under certain hypotheses the empirical law of eigenvalues of a sequence of random real symmetric matrices converges weakly in probability to its mean we then examine the optimal constants in the lsis for the convolved measures in terms of the variance of the convolving gaussian we conclude with partial results on the extension of our main theorem to higher dimensions

cutoff for the ising model on the lattice introduced in 1963 glauber dynamics is one of the most practiced and extensively studied methods for sampling the ising model on lattices it is well known that at high temperatures the time it takes this chain to mix in l 1 on a system of size n is o logn whether in this regime there is cutoff i e a sharp transition in the l 1 convergence to equilibrium is a fundamental open problem if so as conjectured by peres it would imply that mixing occurs abruptly at c o 1 logn for some fixed c 0 thus providing a rigorous stopping rule for this mcmc sampler however obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple markov chains already for the one dimensional ising model showing cutoff is a longstanding open problem

uniqueness and global markov property for euclidean fields the case of general polynomial interactions we give a general method for proving uniqueness and global markov property for euclidean quantum fields the method is based on uniform continuity of local specifications proved by using potential theoretical tools and exploitation of a suitable fkg order structure we apply this method to give a proof of uniqueness and global markov property for the gibbs states and to study extremality of gibbs states also in the case of non uniqueness in particular we prove extremality for 2 4 also in the case of non uniqueness and global markov property for weak coupling 2 4 which solves a long standing problem uniqueness and extremality holds also at any point of differentiability of the pressure with respect to the external magnetic field

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

exact image theory for the sommerfeld half space problem part iii general formulation the general sommerfeld problem with both epsilon and mu discontinuous and a source consisting of arbitrarily oriented electric and or magnetic dipoles at the same location is considered in terms of image theory the problem is formulated with electric and magnetic fields instead of potential quantities resulting in a vector transmission line interpretation of the fourier transformed problem the image sources are seen to be located in complex space expressable in terms of a certain basic image current function which was encountered in part ii of this paper on the vertical electric dipole problem the horizontal electric magnetic dipole image is solved and found to consist of both vertical and horizontal current components the image concept is generalized to the most general three dimensional sources as a check the well known reflection coefficient method is obtained as the far field approximation of the present theory

optimal decomposition of covariance matrices for multivariate stochastic models in hydrology a new method is proposed for decomposing covariance matrices that appear in the parameter estimation phase of all multivariate stochastic models in hydrology this method applies not only to positive definite covariance matrices as do the typical methods of the literature but to indefinite matrices too that often appear in stochastic hydrology it is also appropriate for preserving the skewness coefficients of the model variables as it accounts for the resulting coefficients of skewness of the auxiliary noise variables used by the stochastic model given that the latter coefficients are controlled by the decomposed matrix the method is formulated in an optimization framework with the objective function being composed of three components aiming at 1 complete preservation of the variances of variables 2 optimal approximation of the covariances of variables in the case that complete preservation is not feasible due to inconsistent i e not positive definite structure of the covariance matrix and 3 preservation of the skewness coefficients of the model variables by keeping the skewness of the auxiliary variables as low as possible analytical expressions of the derivatives of this objective function are derived which allow the development of an effective nonlinear optimization algorithm using the steepest descent or the conjugate gradient methods the method is illustrated and explored through a real world application which indicates a very satisfactory performance of the method

streamflow simulation a nonparametric approach in this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences streamflow is assumed to be a markov process with time dependence characterized by a multivariate probability density function kernel methods are used to estimate this multivariate density function simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function this is a nonparametric method for the synthesis of streamflow that is data driven and avoids prior assumptions as to the form of dependence e g linear or nonlinear and the form of the probability density functions e g gaussian we show using synthetic examples with known underlying models that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence the effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the beaver river in utah

estimation of arma models with seasonal parameters the yule walker equations for arma p q models with periodic parameters are derived from which moment estimates can be obtained specifically for the case of arma p 1 models the periodic autoregressive parameters can be found by solving a system of linear equations while the periodic moving average parameters satisfy a system of equations which can be solved iteratively particular examples are given and comparisons are made between the proposed moment estimates and estimates given previously

a technique for approximating the location of surface and leaky wave poles for a lossy dielectric slab an approximation technique for locating the surface and leaky wave poles for a lossy dielectric slab is presented the problem is reduced to the simultaneous solution of two transcendental equations for each of the perfect magnetic conductor pmc and perfect electric conductor pec cases which is shown to yield a simple approximate solution for the poles and which can subsequently be refined using numerical optimization the technique yields both surface wave and leaky wave poles and results are presented for a typical example to demonstrate the approach the greatest approximation accuracy was observed for surface wave and leaky wave poles well removed from the spectral gap for poles either within or in close proximity to the spectral gap an alternative iterative technique is proposed expressions for the number of proper plus improper surface wave poles in a given problem are also derived

a homotopy method for locating all the poles of a parallel plate waveguide with the pml in this paper a homotopy method for locating all the poles of a parallel plate waveguide with the perfectly matched layer is proposed as is well known the green s functions for an open multilayered medium can be approximated by those for a parallel plate waveguide with the perfectly matched layer while the latter green s functions can be theoretically expressed into series expansions of their own eigenmodes without involving any numerical integrations the homotopy method here is applied for finding the desired mode poles in this method the newton raphson iteration is employed to solve every node equation except the start node equation while the dichotomy method is used to solve the start node equation the roots of the end node equation are just the desired mode poles with the proposed method the green s functions for a lossy or lossless multilayered medium can be efficiently calculated by the corresponding series expansions some numerical examples are provided to examine the robustness and accuracy of the proposed method

simple disaggregation by accurate adjusting procedures a multivariate disaggregation method is developed for stochastic simulation of hydrologie series the method is based on three simple ideas that have been proven effective first it starts using directly a typical par 1 model and keeps its formalism and parameter set which is the most parsimonious among linear stochastic models this model is run for the lower level variables without any reference to the known higher level variables second it uses accurate adjusting procedures to allocate the error in the additive property i e the departure of the sum of lower level variables within a period from the corresponding higher level variable they are accurate in the sense that they preserve explicitly certain statistics or even the complete distribution of lower level variables three such procedures have been developed and studied in this paper both theoretically and empirically third it uses repetitive sampling in order to improve the approximations of statistics that are not explicitly preserved by the adjusting procedures the model owing to the wide range of probability distributions it can handle from bell shaped to j shaped and to its multivariate framework is useful for a plethora of hydrologic applications such as disaggregation of annual rainfall or runoff into monthly or weekly amounts and disaggregation of event rainfall depths into partial amounts of hourly or even less duration such real world hydrologic applications have been explored in this study to test the model performance which has proven very satisfactory

electromagnetic modeling of three dimensional bodies in layered earths using integral equations we have developed an algorithm based on the method of integral equations to simulate the electromagnetic responses of three dimensional bodies in layered earths the inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions a matrix equation is constructed using the electric tensor green s function appropriate to a layered earth and it is solved for the vector current in each cell subsequently scattered fields are found by integrating electric and magnetic tensor green s functions over the scattering currents efficient evaluation of the tensor green s functions is a major consideration in reducing computation time we find that tabulation and interpolation of the six electric and five magnetic hankel transforms defining the secondary green s functions is preferable to any direct hankel transform calculation using linear filters a comparison of responses over elongate three dimensional 3 d bodies with responses over two dimensional 2 d bodie

a representation of spatial cross correlations in large stochastic seasonal streamflow models pereira et al 1984 presented a special disaggregation procedure for generating cross correlated monthly flows at many sites while using what are essentially univariate disaggregation models for the flows at each site this was done by using a nonparametric procedure for constructing residual innovations or noise vectors with cross correlated components this note considers the theoretical underpinnings of that streamflow disaggregation procedure and a proposed variation and their ability to reproduce the observed historical cross correlations among concurrent monthly flows at nine brazilian stations

a nearest neighbor bootstrap for resampling hydrologic time series a nonparametric method for resampling scalar or vector valued time series is introduced multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed the motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping resampling it with replacement the method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form e g linear or nonlinear of dependence and the form of the probability density function e g gaussian such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data connections of the nearest neighbor bootstrap to markov processes as well as its utility in a general monte carlo setting are discussed applications to resampling monthly streamflow and some synthetic data are presented the method is shown to be effective with time series generated by linear and nonlinear autoregressive models the utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated

on equivalence of spin and field pictures of lattice systems we investigate the spin and field systems on a lattice connected by the kac siegert transform it is shown that the structures of corresponding theories are equivalent in the sense of isomorphy of space of gibbs states and order parameters using the idea of equivalence of spin and field pictures we exhibit a class of lattice systems possessing infinitely uncountably many ground states the systems of this type with infinite range slow decaying interactions are expected to have a spin glass phase transition

application of dcim to mpie mom analysis of 3d pec objects in multilayered media the formulation c green s functions for multilayered media are reformulated in this paper to extract z dependent part when the source and observation points are in different layers the discrete complex image method dcim is applied to obtain complex images independent on z but dependent on z spl acute for simulation of three dimensional 3 d perfectly electrical conduction pec objects penetrating two or more layers tables of complex images are built in a z spl acute grid during the matrix filling stage of the mixed potential integral equation together with method of moments mpie mom the spatial domain green s functions are interpolated from values in the z spl acute grid while these values are calculated from complex images in the z spl acute grid this interpolation scheme is more efficient than those directly storing the spatial domain green s functions numerical examples are given for analyzing a dipole in a two layered media

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

isoperimetry for gibbs measures we show that a strong mixing condition implies a bakry bobkov ledoux inequality for a probability measure on infinite dimensional space

single site monthly streamflow simulation using entropy theory 1 using entropy theory a new method for single site monthly streamflow simulation is developed which is capable of preserving mean standard deviation skewness and lag one correlation the method entails deriving joint and conditional probability density functions using the entropy theory determining the lagrange multipliers using the information obtained from the historical record and then simulating streamflow by sequential sampling from the conditional distribution the advantage of the entropy based method is that it does not make any assumptions about the probability distribution of the streamflow data it can also preserve the cross correlation between streamflow of the last month of the previous year and the first month of the current year and avoid the generation of negative values the method can also be extended to incorporate higher order moments and more lag correlations if needed the disadvantage is that the method will be cumbersome when more statistics need to be preserved and the bimodality that may exist in the empirical probability density function cannot yet be resolved application to the colorado river basin shows that the entropy based method satisfactorily simulates monthly streamflow

hypercontractivity in noncommutative lpspaces we introduce and study a setup for hypercontractivity in the interpolating family of noncommutative lpspaces associated to a locally normal state on an inductive limitc algebra

hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic ising models abstract we describe some results relating the spectral gap and logarithmic sobolev constants we work initially in the context of symmetric diffusions on a finite dimensional manifold and later apply our results to the analysis of certain infinite systems of mildly interacting diffusions

hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n sphere a logarithmic sobolev inequality with respect to the probability measure a 1 x2 12 dx on 1 1 is proved for all 12 from this inequality sharp hypercontractive estimates are derived for the heat semigroups for ultraspherical polynomials and on the n sphere

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

correlation at low temperature i exponential decay abstract the present paper generalizes the analysis in ann h poincare 1 2000 59 math j ams 8 1997 123 of the correlations for a lattice system of real valued spins at low temperature the gibbs measure is assumed to be generated by a fairly general hamiltonian function with pair interaction the novelty as compared to 2 20 is that the single site self energies of the spins are not required to have only a single local minimum and no other extrema our derivation of exponential decay of correlations goes through the spectral analysis of a deformed laplacian closely related to the witten laplacian studied in 2 20 we prove that this laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

the logarithmic sobolev inequality for continuous spin systems on a lattice abstract in this article we give cf theorem 1 6 a sufficient condition on a local specification for the associated gibbs state to satisfy a logarithmic sobolev inequality in the final section cf theorem 3 10 we relate our condition to the type of mixing condition introduced by dobrushin and shlosman in connection with their work on complete analyticity

a theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall generating fine scale time series of intermittent rainfall that are fully consistent with any given coarse scale totals is a key and open issue in many hydrological problems we propose a stationary disaggregation method that simulates rainfall time series with given dependence structure wet dry probability and marginal distribution at a target finer lower level time scale preserving full consistency with variables at a parent coarser higher level time scale we account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths this approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean variance and autocorrelation function acf for a mixed type stochastic process in terms of mean variance and acfs of both continuous and discrete components respectively to achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse scale totals the generated lower level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model to assess model performance we study rainfall process as intermittent with both independent and dependent occurrences where dependence is quantified by the probability that two consecutive time intervals are dry in either case we provide analytical formulations of main statistics of our mixed type disaggregation model and show their clear accordance with monte carlo simulations an application to rainfall time series from real world is shown as a proof of concept

how the unbounded drift shapes the dirichlet semigroups behaviour of non gaussian gibbs measures abstract we investigate the dirichlet operator semigroups of non gaussian gibbs measures on linear spin lattice systems we prove that dirichlet semigroups preserve spaces of l 2 differentiable functions we show how the non linearity and unboundedness of drift term in dirichlet operator affects the structure of the spaces involved

estimation and validation of contemporaneous parma models for streamflow simulation seasonal streamflow series generally exhibit periodicity in the autocovariance structure such periodicity can be represented by parma models i e autoregressive moving average arma models with parameters that vary with the seasons statistical properties of low order models such as the parma 2 2 model are examined the periodic moment equations are derived they can be used to compute the periodic covariance structure of a given model simulation of streamflow at several sites can be done using the contemporaneous parma model the main problem in using such models is to determine the covariance matrices of innovations traditionally this has been done by the method of maximum likelihood however this method generally leads to significant underestimation of the cross correlation of flows a moment estimator is developed herein for the contemporaneous parma 2 2 model along with three approximate moment based estimators for those cases where a feasible moment solution cannot be obtained the applicability of the proposed methods is illustrated by fitting parma models to weekly flow data for two catchments in the ottawa river basin

logarithmic sobolev inequality for lattice gases with mixing conditions let mu lambda l lambda gc denote the grand canonical gibbs measure of a lattice gas in a cube of sizel with the chemical potential and a fixed boundary condition let mu lambda l n c be the corresponding canonical measure defined by conditioning mu lambda l lambda gc on sigma x in lambda eta x n consider the lattice gas dynamics for which each particle performs random walk with rates depending on near by particles the rates are chosen such that for everyn andl fixed mu lambda l n c is a reversible measure suppose that the dobrushin shlosman mixing conditions holds for mu l lambda gc forall chemical potentials we prove that smallint f log fd mu lambda l n c leqq const l 2 d sqrt f for any probability densityf with respect to mu lambda l n c here the constant is independent ofn orl andd denotes the dirichlet form of the dynamics the dependence onl is optimal

log sobolev inequalities for infinite one dimensional lattice systems it is shown that a unique gibbs measure of infinite spin system with short range interaction on one dimensional lattice satisfies log sobolev inequality

a nonlinear disaggregation method with a reduced parameter set for simulation of hydrologic series a multivariate dynamic disaggregation model is developed as a stepwise approach to stochastic disaggregation problems oriented toward hydrologic applications the general idea of the approach is the conversion of a sequential stochastic simulation model such as a seasonal ar 1 into a disaggregation model its structure includes two separate parts a linear step by step moments determination procedure based on the associated sequential model and an independent nonlinear bivariate generation procedure partition procedure the model assures the preservation of the additive property of the actual not transformed variables its modular structure allows for various model configurations two different configurations par 1 and parx 1 both associated with the sequential markov model are studied like the sequential markov model both configurations utilize the minimum set of second order statistics and the marginal means and third moments of the lower level variables all these statistics are approximated by the model with the use of explicit relations both configurations perform well with regard to the correlation of consecutive lower level variables each located in consecutive higher level time steps the parx 1 configuration exhibits better behavior with regard to the correlation properties of lower level variables with lagged higher level variables 27 refs 5 figs 3 tabs

disaggregation procedures for generating serially correlated flow vectors the structure of disaggregation models places severe constraints on the feasible values of the lagged covariance of generated flow vectors a new and simple class of disaggregation models is presented which employ the valencia schaake disaggregation model structure but allow the models innovations to be serially correlated these models can reproduce 1 the covariance matrix of the disaggregated flows 2 their covariance with the upper level flows and 3 reasonable approximations to the lag one covariance of the disaggregated flow vectors given the constraints imposed by a disaggregation approach the mejia rousselle disaggregation model is shown in general to fail to reproduce the anticipated variances and covariances of the disaggregated flows because the model and its parameter estimators are not self consistent the paper closes with a discussion of practical modeling considerations and of staged disaggregation procedures which reduce the size of multisite multiseason models

dobrushin uniqueness theorem and logarithmic sobolev inequalities we formulate a condition on a local specification e on a countable product space m m being a riemannian manifold or a discrete set 1 1 assuring that the corresponding set of gibbs measures consists of a unique measure satisfying a logarithmic sobolev inequality

a nonparametric approach for representing interannual dependence in monthly streamflow sequences 1 the estimation of risks associated with water management plans requires generation of synthetic streamflow sequences the mathematical algorithms used to generate these sequences at monthly timescales are found lacking in two main respects inability in preserving dependence attributes particularly at large seasonal to interannual time lags and a poor representation of observed distributional characteristics in particular representation of strong asymmetry or multimodality in the probability density function proposed here is an alternative that naturally incorporates both observed dependence and distributional attributes in the generated sequences use of a nonparametric framework provides an effective means for representing the observed probability distribution while the use of a variable kernel ensures accurate modeling of streamflow data sets that contain a substantial number of zero flow values a careful selection of prior flows imparts the appropriate short term memory while use of an aggregate flow variable allows representation of interannual dependence the nonparametric simulation model is applied to monthly flows from the beaver river near beaver utah and the burrendong dam inflows new south wales australia

a very simple proof of the lsi for high temperature spin systems abstract we present a very simple proof that the o n model satisfies a uniform logarithmic sobolev inequality lsi if the difference between the largest and the smallest eigenvalue of the coupling matrix is less than n this condition applies in particular to the sk spin glass model at inverse temperature 1 4 it is the first result of rapid relaxation for the sk model and requires significant cancellations between the ferromagnetic and anti ferromagnetic spin couplings that cannot be obtained by existing methods to prove log sobolev inequalities the proof also applies to more general bounded and unbounded spin systems it uses a single step of zero range renormalisation and bakry emery theory for the renormalised measure

uniqueness and the global markov property for euclidean fields the case of general exponential interaction the uniqueness and the global markov property for the regular gibbs measure corresponding to the interaction u lambda varphi lambda int limits lambda d 2 x int d varrho alpha e alpha varphi 0 x for 0 d a probability measure with support in 2 sqrt pi 2 sqrt pi is proved

exact image theory for the sommerfeld half space problem part ii vertical electrical dipole applying the laplace transform the exact distributed image current function is obtained for the classical sommerfeld half space problem with vertical magnetic current source the resulting field integral is well behaved when the image current is situated in complex space unlike previous approximate images the present theory is valid for any distance height of the source frequency and half space parameters it is demonstrated that the present image theory reduces to the well known dipole image at complex depth for large dielectric parameters of the half space also the reflection coefficient method is obtained as a farfield approximation calculation of fields through exact image integration is seen to be simple and accurate and require modest computer capacity and time in an appendix some properties of the multivalued green s function arising from a dipole source in complex space are also studied

uniform and l 2 convergence in one dimensional stochastic ising models we study the rate of convergence to equilibrium of one dimensional stochastic ising models with finite range interactions we donot assume that the interactions are ferromagnetic or that the flip rates are attractive the infinitesimal generators of these processes all have gaps between zero and the rest of their spectra we prove that if one of these processes is observed by means of local observables then the convergence is seen to be exponentially fast with an exponent that is any number less than the spectral gap moreover this exponential convergence is uniform in the initial configuration

critical ising on the square lattice mixes in polynomial time the ising model is widely regarded as the most studied model of spin systems in statistical physics the focus of this paper is its dynamic stochastic version the glauber dynamics introduced in 1963 and by now the most popular means of sampling the ising measure intensive study throughout the last three decades has yielded a rigorous understanding of the spectral gap of the dynamics on mathbb z 2 everywhere except at criticality while the critical behavior of the ising model has long been the focus for physicists mathematicians have only recently developed an understanding of its critical geometry with the advent of sle cle and new tools to study conformally invariant systems

approach to equilibrium of glauber dynamics in the one phase region ii the general case we develop a new method based on renormalization group ideas block decimation procedure to prove under an assumption of strong mixing in a finite cube 0 a logarithmic sobolev inequality for the gibbs state of a discrete spin system as a consequence we derive the hypercontractivity of the markov semigroup of the associated glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes multiples of the cube 0

an inequality for relative entropy and logarithmic sobolev inequalities in euclidean spaces for a class of density functions q x on rn we prove an inequality between relative entropy and the weighted sum of conditional relative entropies of the following form d p q const i 1n i d pi y1 yi 1 yi 1 yn qi y1 yi 1 yi 1 yn for any density function p x on rn where pi y1 yi 1 yi 1 yn and qi x1 xi 1 xi 1 xn denote the local specifications of p respectively q and i is the logarithmic sobolev constant of qi x1 xi 1 xi 1 xn thereby we derive a logarithmic sobolev inequality for a weighted gibbs sampler governed by the local specifications of q moreover the above inequality implies a classical logarithmic sobolev inequality for q as defined for gaussian distribution by gross this strengthens a result by otto and reznikoff the proof is based on ideas developed by otto and villani in their paper on the connection between talagrand s transportation cost inequality and logarithmic sobolev inequality

conditional parametric models for storm sewer runoff 1 the method of conditional parametric modeling is introduced for flow prediction in a sewage system it is a well known fact that in hydrological modeling the response runoff to input precipitation varies depending on soil moisture and several other factors consequently nonlinear input output models are needed the model formulation described in this paper is similar to the traditional linear models like final impulse response fir and autoregressive exogenous arx except that the parameters vary as a function of some external variables the parameter variation is modeled by local lines using kernels for local linear regression as such the method might be referred to as a nearest neighbor method the results achieved in this study were compared to results from the conventional linear methods fir and arx the increase in the coefficient of determination is substantial furthermore the new approach conserves the mass balance better hence this new approach looks promising for various hydrological models and analysis

a generalized mathematical framework for stochastic simulation and forecast of hydrologic time series a generalized framework for single variate and multivariate simulation and forecasting problems in stochastic hydrology is proposed it is appropriate for short term or long term memory processes and preserves the hurst coefficient even in multivariate processes with a different hurst coefficient in each location simultaneously it explicitly preserves the coefficients of skewness of the processes the proposed framework incorporates short memory autoregressive moving average and long memory fractional gaussian noise models considering them as special instances of a parametrically defined generalized autocovariance function more comprehensive than those used in these classes of models the generalized autocovariance function is then implemented in a generalized moving average generating scheme that yields a new time symmetric backward forward representation whose advantages are studied fast algorithms for computation of internal parameters of the generating scheme are developed appropriate for problems including even thousands of such parameters the proposed generating scheme is also adapted through a generalized methodology to perform in forecast mode in addition to simulation mode finally a specific form of the model for problems where the autocorrelation function can be defined only for a certain finite number of lags is also studied several illustrations are included to clarify the features and the performance of the components of the proposed framework

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

periodic gamma autoregressive processes for operational hydrology a number of models have been suggested for hydrologic time series in general and streamflow series in particular most of them are normal autoregressive ar of order 1 with either constant or periodic parameters since generally hydrologic time series are nonnormal skewed transformations have been suggested to make the series approximately normal a new class of univariate models is proposed herein which incorporates skewed and correlation properties within the model structure without the necessity of transformations such models assume a gamma marginal distribution and a constant or periodic autoregressive structure the models may be additive gamma multiplicative gamma or a mixed model which incorporates properties of both additive and multiplicative models the gamma models were tested and compared in relation to transformed normal ar models by computer simulation studies based on five weekly streamflow series with samples varying from 35 to 40 years of record the results show that the new class of gamma models compares favorably with respect to the normal models in reproducing the basic statistics usually analyzed for streamflow simulation it is expected that the proposed gamma models will be of interest to other researchers for further developments and applications to hydrologic and geophysical time series

estimating correlations in multivariate streamflow models multivariate log normal distributions are often used to model and generate multisite and multiseason streamflow sequences a monte carlo study evaluated alternative estimators of the cross correlation between autocorrelated streamflow series and the lag 1 autocorrelation of a single series when some or all of the flows have a log normal distribution generally smaller mean square error estimates of the correlations of flows are obtained by using the variances and covariances of the flow s logarithms to estimate a streamflow model s parameters sometimes it is advantageous to prewhiten two series before calculating their cross correlation and to unbias the estimated autocorrelation of the streamflow s logarithms

invariance implies gibbsian some new results we investigate stationary distributions of stochastic gradient systems in riemannian manifolds and prove that under certain assumptions such distributions are symmetric these results are extended to countable products of finite dimensional manifolds and applied to gibbs distributions in the case where the single spin spaces are riemannian manifolds in particular we obtain a new result concerning the question whether all invariant measures are gibbsian actually we consider a more general object weak elliptic equations for measures which on the one hand yields the results obtained stronger than the above mentioned statements and on the other hand enables us to give simpler proofs of more general than previously known facts applications to concrete models of lattice systems over d with not necessarily compact spin space are presented also in the case d 3 under certain assumptions of decay of interaction

coupling stochastic models of different timescales a methodology is proposed for coupling stochastic models of hydrologic processes applying to different timescales so that time series generated by the different models be consistent given two multivariate time series generated by two separate unrelated stochastic models of the same hydrologic process each applying to a different timescale a transformation is developed referred to as a coupling transformation that appropriately modifies the time series of the lower level finer timescale so that this series becomes consistent with the time series of the higher level coarser timescale without affecting the second order stochastic structure of the former and also establishes appropriate correlations between the two time series the coupling transformation is based on a developed generalized mathematical proposition which ensures preservation of marginal and joint second order statistics and of linear relationships between lower and higher level processes several specific forms of the coupling transformation are studied from the simplest single variate to the full multivariate in addition techniques for evaluating parameters of the coupling transformation based on second order moments of the lower level process are studied furthermore two methods are proposed to enable preservation of the skewness of the processes in addition to that of second order statistics the overall methodology can be applied to problems involving disaggregation of annual to seasonal and seasonal to subseasonal timescales as well as problems involving finer timescales e g daily to hourly with the only requirement that a specific stochastic model is available for each involved timescale the performance of the methodology is demonstrated by means of a detailed numerical example

on the location of proper and improper surface wave poles for the grounded dielectric slab microstrip antennas a recently obtained closed form asymptotic representation due to s barkeshli 1988 of the microstrip surface green s function is known to provide an efficient moment method analysis of microstrip problems however in order to make this closed form expression accurate even for very small separation of source and field points to within a few tenths of a wavelength both the proper and improper surface wave transition effects must be included in the solution this requires finding the location of the corresponding proper and improper poles a good initial estimate that allows the poles to be located rapidly by using an iterative procedure is presented the number of proper and improper surface wave poles that have to be considered and their values are tabulated

locating all the modes of green s function for a three layered medium based on the path tracking algorithm through a mathematical analysis on the relationship between the characteristic equations of the microstrip geometry and a configuration with a three layered medium a method based on the path tracking algorithm is proposed for precisely locating all the modes for a three layered medium with moderate thickness including surface wave modes leaky wave modes and improper real modes with this method the difficulty caused by branch points and cuts in the contour integral method could be avoided this method can be applied not only in the discrete complex image method dcim but also in the steepest descent path sdp method the proposed method can be extended to more complicated configurations

cutoff for general spin systems with arbitrary boundary conditions the cutoff phenomenon describes a sharp transition in the convergence of a markov chain to equilibrium in recent work the authors established cutoff and its location for the stochastic ising model on the d dimensional torus n d for any d 1 the proof used the symmetric structure of the torus and monotonicity in an essential way here we enhance the framework and extend it to general geometries boundary conditions and external fields to derive a cutoff criterion that involves the growth rate of balls and the log sobolev constant of the glauber dynamics in particular we show there is cutoff for the stochastic ising model on any sequence of bounded degree graphs with subexponential growth under arbitrary external fields provided the inverse log sobolev constant is bounded for lattices with homogenous boundary such as all plus we identify the cutoff location explicitly in terms of spectral gaps of infinite volume dynamics on half plane intersections analogous results establishing cutoff are obtained for nonmonotone spin systems at high temperatures including the gas hard core model the potts model the antiferromagnetic potts model and the coloring model 2014 wiley periodicals inc