asymptotically efficient estimation of models defined by convex moment inequalities this paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest in such a setting the identified set is itself convex and hence fully characterized by its support function we provide conditions under which despite being an infinite dimensional parameter the support function admits n consistent regular estimators a semiparametric efficiency bound is then derived for its estimation and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions in addition we show that the plug in estimator is efficient and devise a consistent bootstrap procedure for estimating its limiting distribution the setting we examine is related to an incomplete linear model studied in beresteanu and molinari 2008 and bontemps magnac and maurin 2012 which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem

conformal invariance and critical dynamics the author discusses the behaviour of dynamic correlation functions under conformal transformations in particular the exact form of the dynamic scaling function at the critical point for an arbitrary isotropic two dimensional model is obtained with either conserved or nonconserved order parameter

efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors abstract let y x e where is unknown and e e x 0 with positive probability but there exist instrumental variables w such that e e w 0 w p 1 it is well known that such nonparametric regression models are generally ill posed in the sense that the map from the data to is not continuous in this paper we derive the efficiency bounds for estimating certain linear functionals of without assuming itself to be identified

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

finitized conformal spectrum of the ising model on the cylinder and torus abstract the spectrum of the critical ising model on a lattice with cylindrical and toroidal boundary conditions is calculated by commuting transfer matrix methods using a simple truncation procedure we obtain the natural finitizations of the conformal spectra recently proposed by melzer these finitizations imply polynomial identities which in the large lattice limit give rise to the rogers ramanujan identities for the c 1 2 virasoro characters

conformal invariance and the critical behavior of the triplet xy quantum chain we introduce and study the critical properties of the tripletxy quantum chain this system is described in terms of three spin interactions and is the generalization of the standardxy quantum chain we show that this model with periodic boundaries has a local gauge invariance and can be described by the composition of two triplet ising models with general toroidal boundary conditions from this composition the phase diagram as well the conformai anomaly and critical exponents are determined by exploring their relations with the mass gap amplitudes predicted by conformai invariance

gel estimation for heavy tailed garch models with robust empirical likelihood inference abstract we construct a generalized empirical likelihood estimator for a garch 1 1 model with a possibly heavy tailed error the estimator imbeds tail trimmed estimating equations allowing for over identifying conditions asymptotic normality efficiency and empirical likelihood based confidence regions for very heavy tailed random volatility data we show the implied probabilities from the tail trimmed continuously updated estimator elevate weight for usable large values assign large but not maximum weight to extreme observations and give the lowest weight to non leverage points we derive a higher order expansion for gel with imbedded tail trimming gelitt which reveals higher order bias and efficiency properties available when the garch error has a finite second moment higher order asymptotics for gel without tail trimming requires the error to have moments of substantially higher order we use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample we also present robust versions of generalized empirical likelihood ratio wald and lagrange multiplier tests and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation finally we present a broad simulation study for gel and gelitt and demonstrate profile weighted expected shortfall for the russian ruble us dollar exchange rate we show that tail trimmed cue gmm dominates other estimators in terms of bias mse and approximate normality

nonuniversal critical behaviour in planar ising models with extended radially symmetric defects using conformal mapping and finite size scaling the authors determine the local magnetic exponent near a defect characterized by couplings of the form j r j 1 a r in accordance with phenomenological considerations they find that it depends continuously on the amplitude a both for a defect in the interior and on the boundary

bulk and surface critical behavior of the three dimensional ising model and conformal invariance using a continuous cluster monte carlo algorithm we investigate the critical three dimensional ising model in its anisotropic limit from the ratio of the magnetic correlations in the strong and the weak coupling directions we determine the length ratio relating the isotropic ising model and the anisotropic limit on this basis we simulate the critical ising model on a spherocylinder s2 x r1 i e a curved geometry obtained from a conformal mapping of the infinite space r3 from correlation lengths along the spherocylinder combined with the prediction of conformal invariance we estimate the magnetic and thermal scaling dimensions as x h 0 5182 6 and x t 1 419 7 respectively the behavior of the binder cumulant is also determined in the limit of an infinitely long spherocylinder next free boundary conditions are imposed on the equators of the spherocylinder and thus the geometry s1 x s x r1 is obtained the surface magnetic scaling dimension is estimated as x s h 1 263 5 the consistency of the aforementioned estimations and existing results confirms that the three dimensional ising model is conformally invariant further the precision of these results reveals that as in two dimensions conformal mappings provide a powerful tool to investigate critical phenomena with the continuous cluster algorithm we also perform simulations of systems inside a conventional solid cylinder the surface magnetic correlation length differs within the estimated error margin by a factor pi 2 from that along a half spherocylinder s1 x s x r1 with the same radius

testing parameters in gmm without assuming that they are identified we propose a generalized method of moments gmm lagrange multiplier statistic i e the k statistic that uses the jacobian at the evaluated parameter value instead of the expected jacobian to obtain its limit behavior we use a novel assumption that brings gmm closer to maximum likelihood and which is easily satisfied the usual asymptotic x2 distribution of the k statistic then holds under a wider set of circumstances like weak and many instrument asymptotics and combinations thereof than the standard full rank case for the jacobian the behavior of the k statistic can be spurious around inflexion points and the maximum of the objective function since the moment conditions are then not satisfied combinations of the k statistic with statistics that test the validity of the moment equations overcome the spurious behavior we conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series

efficient estimation in models with independence restrictions abstract unconditional and conditional independence restrictions are used in many econometric models to identify their parameters however there are few results about efficient estimation procedures for finite dimensional parameters under these independence restrictions this paper computes the efficiency bound for finite dimensional parameters under independence restrictions and proposes an estimator that is consistent asymptotically normal and which achieves the efficiency bound the estimator is based on a growing number of zero covariance conditions that are asymptotically equivalent to the independence restriction the results are illustrated with examples including an instrumental variables regression model and partially linear regression models a small monte carlo study is performed to investigate the estimator s small sample properties and to quantify the efficiency gains that can be made by using the proposed efficient estimator

multicriticality in a self dual potts model the authors explore the self dual plane of a two dimensional potts model with vacancies and four spin interactions using finite size scaling of transfer matrix results since the transfer matrix construction is based on the random cluster representation of the potts model its application is not restricted to an integer number q of potts states for q or 4 the self dual plane contains a critical region belonging to the ordinary potts universality class and a region of first order transition points the two regions are separated by a line of which a range consists of potts tricritical points while another range is of a first order nature the point separating these two ranges is for 0 q or 9 4 identified with the multicritical point of which an exact solution has recently been given by nienhuis et al 1979

toward a conformal field theory for schramm loewner evolutions we discuss the partition function point of view for chordal schramm loewner evolutions and their relationship with correlation functions in conformal field theory both are closely related to crossing probabilities and interfaces in critical models in two dimensional statistical mechanics we gather and supplement previous results with different perspectives point out remaining difficulties and suggest directions for future studies

calogero sutherland eigenfunctions with mixed boundary conditions and conformal field theory correlators we construct certain eigenfunctions of the calogero sutherland hamiltonian for particles on a circle with mixed boundary conditions that is the behavior of the eigenfunction as neighbouring particles collide depend on the pair of colliding particles this behavior is generically a linear combination of two types of power laws depending on the statistics of the particles involved for fixed ratio of each type at each pair of neighboring particles there is an eigenfunction the ground state with lowest energy and there is a discrete set of eigenstates and eigenvalues the excited states and the energies above this ground state we find the ground state and special excited states along with their energies in a certain class of mixed boundary conditions interpreted as having pairs of neighboring bosons and other particles being fermions these particular eigenfunctions are characterised by the fact that they are in direct correspondence with correlation functions in boundary conformal field theory we expect that they have applications to measures on certain configurations of curves in the statistical o n loop model the derivation although completely independent from results of conformal field theory uses ideas from the coulomb gas formulation

estimation of variable coefficients in parabolic distributed systems we present techniques based on cubic spline approximations for estimating coefficients e g diffusion convector velocity etc depending on time and the spatial variable in parabolic distributed systems such as those that arise in transport models convergence results and a summary of numerical performance of the resulting algorithms are given

finite size scaling for correlations of quantum spin chains at criticality we study the finite size scaling behavior of two point correlation functions of translationally invariant many body systems at criticality we propose an efficient method for calculating the two point correlation functions in the thermodynamic limit from numerical data of finite systems our method is most effective when applied to a two dimensional classical system which possesses a conformal invariance by using this method with numerical data obtained from exact diagonalizations and monte carlo simulations we study the spin spin correlations of the quantum spin 1 2 and 3 2 antifierromagnetic chains in particular the logarithmic corrections to power law decay of the correlation of the spin 1 2 isotropic heisenberg antiferromagnetic chain are studied thoroughly we clarify the cause of the discrepancy in previous calculations for the logarithmic corrections our result strongly supports the field theoretic prediction based on the mappings to the wess zumino witten nonlinear model or the sine gordon model we also treat logarithmic corrections and crossover phenomena in the spin spin correlation of the spin 3 2 isotropic heisenberg antiferromagnetic chain our results are consistent with the affleck haldane prediction that the correlation of the spin 3 2 chain exhibits a crossover to the same asymptotic behavior as in the spin 1 2 chain

finite size effects at 2d ising critical points via conformal mapping using recent results by cardy 1984 based on conformal invariance of critical correlation functions the authors calculate universal results for scattering functions s k susceptibilities correlation lengths and specific heat correction terms for finite ising systems in two dimensions with circular elliptical and rectangular shapes and free boundary conditions results show the effects of critical order on these quantities for a circle s k decays as 1 k2 eta for a large range of intermediate k values with an apparent exponent eta 0 09 the probable influence of end edge and domain wall effects in the rectangular geometry is discussed application of the results to experimental systems and other theoretical models is discussed

efficient derivative pricing by the extended method of moments in this paper we introduce the extended method of moments xmm estimator this estimator accommodates a more general set of moment restrictions than the standard generalized method of moments gmm estimator more specifically the xmm differs from the gmm in that it can handle not only uniform conditional moment restrictions i e valid for any value of the conditioning variable but also local conditional moment restrictions valid for a given fixed value of the conditioning variable the local conditional moment restrictions are of special relevance in derivative pricing to reconstruct the pricing operator on a given day by using the information in a few cross sections of observed traded derivative prices and a time series of underlying asset returns the estimated derivative prices are consistent for a large time series dimension but a fixed number of cross sectionally observed derivative prices the asymptotic properties of the xmm estimator are nonstandard since the combination of uniform and local conditional moment restrictions induces different rates of convergence parametric and nonparametric for the parameters

logarithmic corrections for the percolative properties of the four state potts model clusters in the potts model are connected sets of nearest neighbour sites for which the spin variables are in the same state droplets can be obtained by adding bonds with probability p 1 exp k between the sites in a cluster where k is the potts model s inverse temperature when q to 4 renormalization group rg fixed points describing clusters and droplets will coalesce leading to logarithmic corrections we calculate the precise form of these corrections used in a differential rg method our predictions are then tested using extensive monte carlo calculations theory and the simulations are found to be in excellent agreement

corner transfer matrix of generalized free fermion vertex systems the hamiltonian limit of the corner transfer matrix ctm of a generalized free fermion vertex system of finite size leads to a quantum spin hamiltonian of the particular form hn sigma n 1n 1 n sigma nx sigma n 1x lambda sigma ny sigma n 1y h sigma nz sigma sub n 1z diagonalization may be achieved for all pairs of parameters lambda h with the use of some new elliptic polynomials which extend the class of special polynomials known so far in the context of ctm

inverse scattering on half line the theory of inverse scattering on half line has been presented in the literature we give a new approach to the theory and analyze its logic in particular we prove that the potential reconstructed from the given scattering data generates the scattering data identical with the original data that the scattering data obtained from the given potential generate the potential which is identical with the original one that the normalizing constants can be put in a bijective correspondence to the parameters which define the general solution to the marchenko equation for x 0 we give a new characterization of the scattering data this characterization does not involve assumptions about the number of solutions to some integral equations in contrast with the known one applications of the theory are given necessary and sufficient conditions on the scattering data for q to be compactly supported or for q to be in l2 existence of a q c0 0 r which produces infinitely many purely imaginary resonances etc

universal order parameter profiles in confined critical systems with boundary fields the authors consider systems at the bulk critical temperature with an ordering field applied at the boundary for various boundary geometries universal expressions for the spatial dependence of the order parameter are obtained by conformal mapping of the known results for the half space analytical results for strip wedge and other two dimensional geometries and for systems with spherical boundaries in arbitrary dimension are given

semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions abstract this paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions our results extend those of chamberlain 1992b and ai and chen 2003 for semiparametric conditional moment restrictions with identical information sets to the case of nested information sets and those of chamberlain 1992a and brown and newey 1998 for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables our results are applicable to semiparametric panel data models and two stage plug in problems as an important example we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables regression npiv and find that simple plug in npiv estimators are not efficient we present an optimally weighted orthogonalized sieve minimum distance estimator that achieves the semiparametric efficiency bound

six vertex model with rotated boundary conditions we investigate the six vertex model on a square lattice rotated through an arbitrary angle with respect to the coordinate axes a model recently introduced by litvin and priezzhev auxiliary vertices are used to define an inhomogeneous system which leads to a one parameter family of commuting transfer matrices a product of commuting transfer matrices can be interpreted as a transfer matrix acting on zigzag walls in the rotated system using an equation for commuting transfer matrices we calculate their eigenvalues finite size properties of the model are discussed from the viewpoint of the conformal field theory

conformal invariance of spin correlations in the planar ising model we rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi point spin correlations in the critical ising model on arbitrary simply connected planar domains this solves a number of conjectures coming from the physical and the mathematical literature the proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques

neglected heterogeneity in moment condition models abstract the central concern of this paper is parameter heterogeneity in models specified by a number of unconditional or conditional moment conditions and thereby the provision of a framework for the development of apposite optimal m tests against its potential presence we initially consider the unconditional moment restrictions framework optimal m tests against moment condition parameter heterogeneity are derived with the relevant jacobian matrix obtained in terms of the second order own derivatives of the moment indicator in a leading case gmm and gel tests of specification based on generalized information matrix equalities appropriate for moment based models are described and their relation to optimal m tests against moment condition parameter heterogeneity examined a fundamental and important difference is noted between gmm and gel constructions the paper is concluded by a generalization of these tests to the conditional moment context and the provision of a limited set of simulation experiments to illustrate the efficacy of the proposed tests

local state probabilities for an infinite sequence of solvable lattice models the authors present a new infinite sequence of solvable lattice models they contrast strikingly with the eight vertex solid on solid models and admit extra degrees of freedom for the local fluctuation variables the exact one point functions are obtained the result is neatly described in terms of theta function identities using their modular invariance critical behaviour is studied and exponents evaluated

conformal theory of a next nearest neighbour interaction model abstract a one dimensional quantum model with generalized next nearest neighbour interaction is studied and its conformal field theory is constructed the numerical results convince us of the existence of a critical phenomenon in this model the critical point condition and the value of the central charge c are given also the anomalous scaling dimensions of the conformal field are given

self avoiding walks near an excluded line the problem of a saw starting next to an excluded line say the negative x axis is studied in two dimensions using arguments based on conformal invariance and scaling it is shown that the moments of the displacement along the x axis after n steps xn grow like x2k 1n approximately n 2k 1 v the argument can however be simplified and extended also to the case of three dimensions

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

gel statistics under weak identification abstract the central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification to this end we develop pearson type test statistics based on gel implied probabilities formed from general kernel smoothed versions of the moment indicators we also modify the statistics suggested in guggenberger and smith 2008 for a general kernel smoothing function importantly for our conclusions we provide gel time series counterparts to gmm and gel conditional likelihood ratio statistics given in kleibergen 2005 and smith 2007 our analysis not only demonstrates that these statistics are asymptotically conditionally pivotal under both classical asymptotic theory and weak instrument asymptotics of stock and wright 2000 but also provides asymptotic power results in the weakly identified time series context consequently the empirical null rejection probabilities of the associated tests and thereby the coverage probabilities of the corresponding confidence regions should not be affected greatly by the strength or otherwise of identification a comprehensive monte carlo study indicates that a number of the tests proposed here represent very competitive choices in comparison with those suggested elsewhere in the literature

cft estimates of the universal binder parameter for quantum ground state transitions in one dimension the universal values of the equal time binder parameter for quantum ground state transitions in one dimension are predicted with the help of the conformal field theory cft in two dimensions the values are compared with the results from the numerical diagonalization of the s 1 antiferromagnetic xxz chain it is found that the finite size corrections may be of a higher order in l 1 than expected

semi parametric estimation of american option prices abstract we introduce a novel semi parametric estimator of american option prices in discrete time the specification is based on a parameterized stochastic discount factor and is nonparametric w r t the historical dynamics of the markovian state variables the historical transition density estimator minimizes a distance built on the kullback leibler divergence from a kernel transition density subject to the no arbitrage restrictions for a non defaultable bond the underlying asset and some american option prices we use dynamic programming to make explicit the nonlinear restrictions on the euclidean and functional parameters coming from option data we study asymptotic and finite sample properties of the estimators

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

non analytic finite size corrections for the heisenberg chain in a magnetic field with free and twisted boundary conditions the finite size energy spectrum of the anisotropic heisenberg chain in an external magnetic field is calculated for free and twisted boundary conditions as with periodic boundary conditions it is found that the spectra exhibit non analytical terms which do not fit into the form predicted on the basis of conformal invariance unless extra commensurability conditions between the size of the system and the external field are introduced taking these conditions into account some scaling dimensions for associated models are derived

supersymmetric two dimensional toda lattice the two dimensional toda lattice connected with contragradient lie superalgebras is studied the systems of linear equations associated with the models for which the inverse scattering method is applicable are written down the reduction group is calculated

possibly exact fractal dimensions from conformal invariance based on an equivalence between the q state potts model and conformally invariant field theories the author speculates that all fractal dimensionalities of two dimensional percolation are given by the formula d 100 x2 48 where x is an integer the same formula should also apply to self avoiding walks and lattice animals this approach is extended to cluster weighted percolation his conjecture seems to agree with previous exact and numerical results except for the backbone exponent and possibly for lattice animals

finite size scaling and conformal invariance in a self dual quantum z 5 model considers the critical behaviour of a particular set of onedimensional self dual models with z n symmetry n or 5 the critical indices are evaluated using standard finite size scaling and by exploiting their relations with the mass gap amplitudes predicted by conformal invariance the results strongly suggest that the recently introduced z n quantum field theory is the underlying field theory for these statistical mechanics models

inversion theory for parameterized diffusion problem invertibility is established for the mathematical formulation most often used to describe the one dimensional magnetotelluric problem and related nondestructive testing techniques using the terminology of the applications for a large space of conductivity functions with no analyticity requirements recovery of the conductivity function from magnetotelluric data is shown to be unique

estimating features of a distribution from binomial data we propose estimators of previous termfeatures of the distributionnext term of an unobserved random variable w what is observed is previous termanext term sample of y v x where previous termanext term binary y equals one when w exceeds previous termanext term threshold v determined by experimental design and x are covariates potential applications include bioassay and destructive duration analysis our empirical application is referendum contingent valuation in resource economics where one is interested in previous termfeatures of the distributionnext term of values w willingness to pay placed by consumers on previous termanext term public good such as endangered species sample consumers with characteristics x are asked whether they favor with y 1 if yes and zero otherwise previous termanext term referendum that would provide the good at previous termanext term cost v specified by experimental design this paper provides estimators for quantiles and conditional on x moments of w under both nonparametric and semiparametric specifications

assessing misspecified asset pricing models with empirical likelihood estimators abstract hansen and jagannathan 1997 compare misspecified asset pricing models based on least square projections on a family of admissible stochastic discount factors we extend their fundamental contribution by considering minimum discrepancy projections where misspecification is measured by a family of convex functions that take into account higher moments of asset returns the minimum discrepancy problems are solved on dual spaces producing a family of estimators that captures the least square problem as a particular case we derive the asymptotic distributions of the estimators for the cressie read family of discrepancies and illustrate their use with an assessment of the consumption asset pricing model

efficiency bounds for missing data models with semiparametric restrictions this paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random mar coincides with that of a particular augmented moment condition problem the augmented system consists of the inverse probability weighted ipw original moment restriction and an additional conditional moment restriction which exhausts all other implications of the mar assumption the paper also investigates the value of additional semiparametric restrictions on the conditional expectation function cef of the original moment function given always observed covariates in the program evaluation context for example such restrictions are implied by semiparametric models for the potential outcome cefs given baseline covariates the efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem some implications of these results for estimation are briefly discussed

the critical behaviour of self dual z n spin systems finite size scaling and conformal invariance this paper is concerned with the critical properties of a family of self dual two dimensional z n models whose bulk free energy is exactly known at the self dual point the author s analysis is performed by studying the finite size behaviour of the corresponding one dimensional quantum hamiltonians which also possess an exact solution at their self dual point by exploring finite size scaling ideas and the conformal invariance of the critical infinite system the author calculates for n up to 8 the critical temperature and critical exponents as well as the central charge associated with the underlying conformal algebra the results strongly suggest that the z n quantum field theory of zamolodchikov and fateev is the underlying field theory associated with these statistical mechanical systems the author also tests for the z 5 case the conjecture that these models correspond to the bifurcation points in the phase diagram of the general z n spin model where a massless phase originates

fisher renormalisation and conformal field theory abstract the fisher renormalisation of critical exponents caused by addition of constrained annealing hidden variables to a system is investigated within conformal field theory the standard unitary su 2 conformal field theory does not allow for fisher renormalisation and extended unitary conformal field theories are instead investigated these are provided by explicit constructions based on coupling the energy operator to new degrees of freedom in a conformally invariant way they lead to new families of generalised model including fisher renormalised exponents or new renormalisations

test of finite size scaling predictions in three dimensions a constrained monomer dimer cmd model on decorated hypercubic lattices which is exactly solvable in any dimensionality d is studied the model is critical in the limit of maximal packing of the dimer configurations allowed by the constraint for d 2 it is equivalent to the rooted tree model on the square lattice considered by duplantier and david 1988 the validity of two finite size scaling predictions in higher dimensionalities is studied 1 the existence of logarithmic corrections in the free energy due to corners and ii the amplitude exponent relation for the pair correlation function the logarithmic finite size corrections are obtained for arbitrary d for boundary conditions which are periodic for d or 0 dimensions and free in the remaining d d dimensions dimer dimer correlation functions are studied at d 3 for a system finite in two dimensions and infinite in the third it is shown that the amplitude exponent relation for the cmd model holds for d 2 and breaks down for d 3

efficient estimation and computation of parameters and nonparametric functions in generalized semi non parametric regression models abstract the efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature bickel et al 1993 in this paper we study efficient estimators for both parameters and nonparametric functions in a class of generalized semi non parametric regression models which cover commonly used semiparametric models such as partially linear models partially linear single index models and two sample semiparametric models we propose a maximum likelihood principle combined with the local linear technique for estimating the parameters and nonparametric functions the proposed estimators of the parameters and a linear functional of the nonparametric functions are consistent and asymptotically normal and are further shown to be semiparametrically efficient an efficient computational algorithm to achieve the maximization is proposed extensive simulation experiments show the superiority of the proposed methods three real data examples are analyzed and presented as an illustration

critical off critical interface in the ising quantum chain and conformal invariance the low energy excitation spectrum of an ising quantum chain in a transverse field which is critical h j 1 for 1 or n or l 2 and off critical h not j for l 2 n or l is calculated up to o l 1 interface critical exponents are determined numerically in the odd sector and exactly in the even sector using finite size scaling one gets an ordinary surface transition when h j and an extraordinary surface transition when h j the gap exponent relation is verified the mass gaps and the level degeneracy are in agreement with conformal invariance

universality in the 2d ising model and conformal invariance of fermionic observables it is widely believed that the celebrated 2d ising model at criticality has a universal and conformally invariant scaling limit which is used in deriving many of its properties however no mathematical proof has ever been given and even physics arguments support a priori weaker mobius invariance we introduce discrete holomorphic fermions for the 2d ising model at criticality on a large family of planar graphs we show that on bounded domains with appropriate boundary conditions those have universal and conformally invariant scaling limits thus proving the universality and conformal invariance conjectures

the numerical solution of an inverse problem for a class of one dimensional diffusion equations with piecewise constant coefficients in this paper an inverse problem for a class of one dimensional diffusion equations with piecewise constant coefficients is studied this problem is solved using an explicit formula for the corresponding spectral measures and an analytic continuation in the complex plane

correlation functions of twist operators applied to single self avoiding loops the o n spin model in two dimensions may equivalently be formulated as a loop model and then mapped to a height model which is conjectured to flow under the renormalization group to a conformal field theory cft at the critical point the order n terms in the partition function and correlation functions describe single self avoiding loops we investigate the ensemble of these self avoiding loops using twist operators which count loops which wind non trivially around them with a factor 1 these turn out to have level 2 null states and hence their correlators satisfy a set of partial differential equations we show that partly connected parts of the four point function count the expected number of loops which separate one pair of points from the other pair and find an explicit expression for this we argue that the differential equation satisfied by these expectation values should have an interpretation in terms of a stochastic schramm loewner evolution sle process with 6 the two point function in a simply connected domain satisfies a closely related set of equations we solve these and hence calculate the expected number of single loops which separate both points from the boundary

a simplified approach to computing efficiency bounds in semiparametric models using some standard hilbert space theory a simplified approach to computing efficiency bounds in semiparametric models is presented we use some interesting examples to illustrate this approach and also obtain some results which seem to be new to the literature

partition functions loop measure and versions of sle we discuss the partition function view of the schramm loewner evolution after reviewing a number of known results in the framework of brownian loop measures and scaling rules for partition functions we give some speculation about multiply connected domains

a new class of asymptotically efficient estimators for moment condition models in this paper we propose a new class of asymptotically efficient estimators for moment condition models these estimators share the same higher order bias properties as the generalized empirical likelihood estimators and once bias corrected have the same higher order efficiency properties as the bias corrected generalized empirical likelihood estimators unlike the generalized empirical likelihood estimators our new estimators are much easier to compute a simulation study finds that our estimators have better finite sample performance than the two step gmm and compare well to several potential alternatives in terms of both computational stability and overall performance

phase structure of the three matrix chain model coupled to the magnetic field the author investigates the critical properties of the three matrix chain model corresponding to the blume emery griffiths model in a homogeneous magnetic field on a fluctuating lattice the third order critical line and the tricritical point disappear after the magnetic field is switched on it is however found that another critical line exists as a result of the naive perturbative expansion and the string susceptibility exponent is 1 3 on the line it is also shown that the critical exponent of the magnetic moment beta is 1 6 which coincides with the kpz solution

a critical amplitude relation for one dimensional quantum transitions and determination of the exponent eta a new critical amplitude relation which holds for one dimensional quantum ground state transitions is presented the relation yields an estimate of the sound velocity which appears in the conformal field theory as an a priori unknown parameter with the use of this relation the exponent eta can be explicitly determined from only the scaling fit of the off critical energy gap the relation is confirmed in the transverse ising model the s 1 2 anisotropic xy model and the three state potts model

conformal invariance and the operator content of the xxz model with arbitrary spin the authors are concerned with the critical properties of the anisotropic heisenberg chain or xxz model with arbitrary integer or half integer spin the eigenspectra of these hamiltonians with periodic boundaries are calculated for finite chains by solving numerically their associated bethe ansatz equations the resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified for lattices with an even and odd number of sites the results for spin 1 and spin 3 2 indicate that the conformal anomaly c for these models in the gapless regime has the value c 3s 1 s independent of the anisotropy and the exponents vary continuously with the anisotropy as in the eight vertex model the operator content of these models indicate that the underlying field theory governing these critical spin s models is described by composite fields formed by the product of gaussian and z n fields with n 2s finally some of the irrelevant operators which produce the leading finite size corrections of the eigenenergies are identified

fractal dimensions of potts clusters potts clusters are connected sets of nearest neighbour sites for which the potts variable is in the same state at criticality there exists a fractal cluster using arguments from the renormalization group conformal invariance and numerical simulations the author determines the bulk surface hull and red bond dimension of these clusters as a function of the number of potts states

the 1 1 do 2 model a finite lattice analysis finite size methods and the theory of conformal invariance are applied to the 1 1 do 2 or x y planar model the critical point is found to be xc approximately 2 0 the value sigma 0 501 or 0 005 is obtained for the index governing the critical divergence of the correlation length and the conformal anomaly is confirmed to be c 1 the kosterlitz thouless features of a low temperature phase with zero spontaneous magnetisation but algebraic decay of correlations together with a standard high temperature phase are observed the critical exponent eta is determined as a function of coupling constant and compared with theoretical expectations

the baxter revolution i review the revolutionary impact rodney baxter has had on statistical mechanics beginning with his solution of the 8 vertex model in 1971 and the invention of corner transfer matrices in 1976 to the creation of the rsos models in 1984 and his continuing current work on the chiral potts model