graphical representations and cluster algorithms i discrete spin systems abstract graphical representations similar to the fk representation are developed for a variety of spin systems in several cases it is established that these representations have fkg monotonicity properties which enables characterization theorems for the uniqueness phase and the low temperature phase of the spin system certain systems with intermediate phases and or first order transitions are also described in terms of the percolation properties of the representations in all cases these representations lead in a natural fashion to swendsen wang type algorithms hence at least in the above mentioned instances these algorithms realize the program described by kandel and domany phys rev b 43 1991 8539 8548 all of the algorithms are shown to satisfy a li sokal bound which at least for systems with a divergent specific heat implies critical slowing down however the representations also give rise to invaded cluster algorithms which may allow for the rapid simulation of some of these systems at their transition points

nonlocal isoperimetric inequalities for kolmogorov fokker planck operators abstract in this paper we establish optimal isoperimetric inequalities for a nonlocal perimeter adapted to the fractional powers of a class of kolmogorov fokker planck operators which are of interest in physics these operators are very degenerate and do not possess a variational structure the prototypical example was introduced by kolmogorov in his 1938 paper on brownian motion and the theory of gases our work has been influenced by ideas of m ledoux in the local case

logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

the covariance matrix of the potts model a random cluster analysis we consider the covariance matrix g mm q2 of thed dimensionalq states potts model rewriting it in the random cluster representation of fortuin and kasteleyn in any of theq ordered phases we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances thereby attributing algebraic significance to these stochastic geometric quantities we also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers for dimensiond 2 we show that this correlation length and the correlation length of the two point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two for systems with first order transitions this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self dual point o for systems with second order transitions this relation implies the equality of the correlation length exponents from above and below threshold as well as an amplitude ratio of two in the course of proving the above results we establish several properties of independent interest including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions and left continuity of the two dimensional free boundary condition percolation probability at o we also introduce dlr equations for the random cluster model and use them to establish ergodicity of the free measure in order to prove these results we introduce a new class of events which we call decoupling events and two inequalities for these events the first is similar to the fkg inequality but holds for events which are neither increasing nor decreasing the second is similar to the van den berg kesten inequality in standard percolation both inequalities hold for an arbitrary fkg measure

a rigorous theory of finite size scaling at first order phase transitions a large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered the dependence of the finite volume magnetizationm per h l in cubes of sizel d under periodic boundary conditions on the external fieldh is analyzed for the case where two phases coexist at the infinite volume transition pointh t we prove that independent of the details of the model the finite volume magnetization per lattice site behaves likem per h t m tanh ml d h ht withm per h denoting the infinite volume magnetization and m 1 2 m per h t 0 m per h t 0 introducing the finite size transition pointh m l as the point where the finite volume susceptibility attains the maximum we show that in the case of asymmetric field driven transitions its shift ish t h m l o l 2d in contrast to claims in the literature starting from the obvious observation that the number of stable phases has a local maximum at the transition point we propose a new way of determining the pointh t from finite size data with a shift that is exponentially small inl finally the finite size effects are discussed also in the case where more than two phases coexist

finite size scaling for potts models recently borgs and koteck developed a rigorous theory of finite size effects near first order phase transitions here we apply this theory to the ferromagneticq state potts model which forq large andd 2 undergoes a first order phase transition as the inverse temperature is varied we prove a formula for the internal energy in a periodic cube of side lengthl which describes the rounding of the infinite volume jump e in terms of a hyperbolic tangent and show that the position of the maximum of the specific heat is shifted by m l inq e l d o l 2d with respect to the infinite volume transition point t we also propose an alternative definition of the finite volume transition temperature t l which might be useful for numerical calculations because it differs only by exponentially small corrections from t

finite size effects for the potts model with weak boundary conditions using the pirogov sinai theory we study finite size effects for the ferromagnetic q state potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions if the surface coupling is about half of the bulk coupling and q is sufficiently large we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume this allows a rigorous control of the finite size effects for these weak boundary conditions in particular we give explicit formulae for the rounding of the infinite volume jumps of the internal energy and magnetization as well as the position of the maximum of the finite volume specific heat while the width of the rounding window is of order l d the same as for periodic boundary conditions the shift is much larger of order l 1 for strong boundary conditions the surface coupling is either close to zero or close to the bulk coupling the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase respectively in particular it means that sufficiently small boundary fields lead to the disordered and not to the ordered gibbs state this gives an explicit proof of a van enter s result that the phase transition in the potts model is not robust

algorithmic pirogov sinai theory we develop an efficient algorithmic approach for approximate counting and sampling in the low temperature regime of a broad class of statistical physics models on finite subsets of the lattice mathbb z d and on the torus mathbb z n mathbb z d our approach is based on combining contour representations from pirogov sinai theory with barvinok s approach to approximate counting using truncated taylor series some consequences of our main results include an fptas for approximating the partition function of the hard core model at sufficiently high fugacity on subsets of mathbb z d with appropriate boundary conditions and an efficient sampling algorithm for the ferromagnetic potts model on the discrete torus mathbb z n mathbb z d at sufficiently low temperature

the strong coupling expansion and the ultra local approximation in field theory abstract we first discuss the strong coupling expansion in 4 d theory and quantum electrodynamics in a d dimensional euclidean space in a formal representation for the schwinger functional we treat the gaussian part of the action as a perturbation with respect to the remaining terms in this way we develop a perturbative expansion around the ultra local model where fields defined at different points of euclidean space are decoupled we examine the singularities of the strong coupling perturbative expansion analysing the analytic structure of the zero dimensional generating functions in the coupling constant complex planes we also discuss the ultra local generating functional in a non polynomial model in field theory defined by the following interaction lagrangian density l ii g 1 g 2 g 1 cosh g 2 x 1 finally we use the strong coupling perturbative expansion to compute the renormalized vacuum energy of the strongly coupled 4 d theory assuming that the scalar field is defined in a region bounded by two parallel hyperplanes where we are imposing dirichlet dirichlet boundary conditions

continuous phase transitions with a convex dip in the microcanonical entropy the appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition however a convex dip also shows up in some systems with a continuous transition as for example in the baxter wu model and in the four state potts model in two dimensions we demonstrate that the appearance of a convex dip in those cases can be traced back to a finite size effect the properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite size scaling theory for continuous phase transitions results obtained from numerical simulations corroborate the predictions of the scaling theory

skeleton inequalities and mean field properties for lattice spin systems we present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential v 2 a 2 2 mn 2 2n 2n 2n a real 2n 0 generalizing the brydges frohlich sokal and bovier felder methods as an application of the inequalities we prove that for sufficiently soft systems in d 4 dimensions critical exponents and 4 take their mean field values i e 1 0 and 4 3 2

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

invaded cluster algorithm for potts models the invaded cluster algorithm a method for simulating phase transitions is described in detail theoretical albeit nonrigorous justification of the method is presented and the algorithm is applied to potts models in two and three dimensions the algorithm is shown to be useful for both first order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities the dynamic properties of the invaded cluster algorithm are studied numerical evidence suggests that the algorithm has no critical slowing for ising models s1063 651x 96 09208 2

the analysis of structural equation models by means of derivative free nonlinear least squares it is shown that the par derivative free nonlinear regression program in bmdp can be used to fit structural equation models producing generalized least squares estimates standard errors and goodness of fit test statistics covariance structure models more general than lisrel can be analyzed the approach is particularly useful for dealing with new non standard models and experimenting with alternate methods of estimation

improper solutions in the analysis of covariance structures their interpretability and a comparison of alternate respecifications a monte carlo approach was employed to investigate the interpretability of improper solutions caused by sampling error in maximum likelihood confirmatory factor analysis four models were studied with two sample sizes of the overall goodness of fit indices provided by the lisrel vi program significant differences between improper and proper solutions were found only for the root mean square residual as expected indicators of the factor on which the negative uniqueness estimate occurred had biased loadings and the correlations of its factor with other factors were also biased in contrast the loadings of indicators on other factors and those factor intercorrelations did not have any bias of practical significance for initial solutions with one negative uniqueness estimate three respecifications were studied fix the uniqueness at 00 fix it at 20 or constrain the domain of the solution to be proper for alternate respecified solutions that were converged and proper the constrained solutions and uniqueness fixed at 00 solutions were equivalent the mean goodness of fit and pattern coefficient values for the original improper solutions were not meaningfully different from those obtained under the constrained and uniqueness fixed at 00 respecifications

fisher zeros and singular behaviour of the two dimensional potts model in the thermodynamic limit the duality transformation is applied to the fisher zeros near the ferromagnetic critical point in the q 4 state two dimensional potts model a requirement that the locus of the duals of the zeros be identical to the dual of the locus of zeros in the thermodynamic limit i recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and ii identifies duality with complex conjugation for the zeros near the ferromagnetic critical point the conjecture that all zeros governing ferromagnetic singular behaviour satisfy the latter requirement gives the full locus of such fisher zeros to be a circle this locus together with the density of zeros is then shown to be sufficient to recover the singular part of the thermodynamic functions in the thermodynamic limit their regular parts coming from separate loci of zeros not crossing the positive real temperature axis

functional inequalities for a class of nonlocal hypoelliptic equations of hormander type abstract we consider a class of second order partial differential operators a of hormander type which contain as a prototypical example a well studied operator introduced by kolmogorov in the 30s we analyse some properties of the nonlocal operators driven by the fractional powers of a and we introduce some interpolation spaces related to them we also establish sharp pointwise estimates of harnack type for the semigroup associated with the extension operator moreover we prove both global and localised versions of poincare inequalities adapted to the underlying geometry

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

finite size scaling for the 2d ising model with minus boundary conditions we study the magnetization m l h for the ising model on a large but finite lattice square under the minus boundary conditions using known large deviation results evaluating the balance between the competing effects of the minus boundary conditions and the external magnetic field h we describe the details of its dependence on h as exemplified by the finite size rounding of the infinite volume magnetization discontinuity and its shift with respect to the infinite volume transition point

how good is good enough in path analysis of fmri data this paper is concerned with the problem of evaluating goodness of fit of a path analytic model to an interregional correlation matrix derived from functional magnetic resonance imaging fmri data we argue that model evaluation based on testing the null hypothesis that the correlation matrix predicted by the model equals the population correlation matrix is problematic because p values are conditional on asymptotic distributional results which may not be valid for fmri data acquired in less than 10 min as well as arbitrary specification of residual variances and effective degrees of freedom in each regional fmri time series we introduce an alternative approach based on an algorithm for automatic identification of the best fitting model that can be found to account for the data the algorithm starts from the null model in which all path coefficients are zero and iteratively unconstrains the coefficient which has the largest lagrangian multiplier at each step until a model is identified which has maximum goodness by a parsimonious fit index repeating this process after bootstrapping the data generates a confidence interval for goodness of fit of the best model if the goodness of the theoretically preferred model is within this confidence interval we can empirically say that the theoretical model could be the best model this relativistic and data based strategy for model evaluation is illustrated by analysis of functional mr images acquired from 20 normal volunteers during periodic performance for 5 min of a task demanding semantic decision and subvocal rehearsal a model including unidirectional connections from frontal to parietal cortex designed to represent sequential engagement of rehearsal and monitoring components of the articulatory loop is found to be irrefutable by hypothesis testing and within confidence limits for the best model that could be fitted to the data

field theory of finite size effects for systems with a one component order parameter the field theoretic renormalization group approach is used to describe finite size effects near the critical point of the 4 model with a one component order parameter problems of previous perturbation approaches for t tc are discussed and an improved perturbation theory is employed that is applicable both above and below tc the susceptibility order parameter specific heat and a cumulant ratio are calculated for fixed d 4 in one loop order for the case of a cube with periodic boundary conditions finite size scaling functions are evaluated in three dimensions without using the e 4 d expansion quantitative agreement with monte carlo mc data of the three dimensional ising model is found in most cases additional mc data of larger systems would be desirable in order to test the detailed predictions of the finite size field theory more conclusively in the asymptotic region

the monotony criterion for a finite size scaling analysis of phase transitions we propose a new criterion to analyze the order of phase transitions within a finite size scaling analysis it refers to response functions like order parameter susceptibilities and the specific heat and states different monotony behavior in volume for first and second order transitions close to the transition point the criterion applies to analytical and numerical studies of phase diagrams including tricritical behavior

using phantom and imaginary latent variables to parameterize constraints in linear structural models the most widely used computer programs for structural equation models analysis are the lisrel series of joreskog and sorbom the only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal rindskopf 1983 showed how these simple properties could be used to represent models with more complicated constraints namely inequality constraints on unique variances in this paper two new concepts are introduced which enable a much wider variety of constraints to be made the concepts phantom and imaginary latent variables allow fairly general equality and inequality constraints on factor loadings and structural model coefficients

least squares estimation of covariance matrices in balanced multivariate variance components models abstract the problem of estimating covariance matrices in balanced multivariate variance components models is discussed as with univariate models it is possible for the traditional estimators based on differences of the mean square matrices to produce estimates that are outside the parameter space in fact in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite nnd in this article we develop an iterative estimation procedure satisfying a least squares criterion that is guaranteed to produce nnd estimates of the covariance matrices discuss the speed of convergence and provide an example to show how the estimates change

a first order phase transition in the three dimensional four state antiferromagnetic potts model studies the four state antiferromagnetic potts model with next nearest neighbour ferromagnetic interactions on the simple cubic lattice by the monte carlo method the ratio j2 j1 of the strength of the next nearest neighbour interactions to that of the nearest neighbour interactions is to be 10 the author analyses the finite size effects of the energy the specific heat the fourth order cumulant the magnetization the susceptibility and the effective transition temperatures with the help of the finite size scaling theory the author concludes that the transition of the model is assigned to be of first order

residual diagnostics for growth mixture models examining the impact of a preventive intervention on multiple trajectories of aggressive behavior growth mixture modeling has become a prominent tool for studying the heterogeneity of developmental trajectories within a population in this article we develop graphical diagnostics to detect misspecification in growth mixture models regarding the number of growth classes growth trajectory means and covariance structures for each model misspecification we propose a different type of empirical bayes residual to quantify the departure our procedure begins by imputing multiple independent sets of growth classes for the sample then from these so called pseudoclass draws we form diagnostic plots to examine the averaged empirical distributions of residuals in each such class our proposals draw on the property that each single set of pseudoclass adjusted residuals is asymptotically normal with known mean and co variance when the underlying model is correct these methods are justified in simulation studies involving two classes of linear growth curves that also differ by their covariance structures

a scale invariant treatment for recursive path models a reparameterization is formulated that yields estimates of scale invariant parameters in recursive path models with latent variables and asymptotically correct standard errors without the use of constrained optimization the method is based on the logical structure of the reticular action model

crossover finite size scaling at first order transitions in a recent paper we developed a method which allows one to control rigorously the finite size behavior in long cylinders near first order phase transitions at low temperature here we apply this method to asymmetric transitions with two competing phases and to theq state potts model as a typical model of a temperature driven transition whereq low temperature phases compete with one high temperature phase we obtain the finite size scaling of the firstn eigenvalues wheren is the number of competing phases of the transfer matrix in a periodic box of volumel l t and as a corollary the finite size scaling of the shape of the order parameter in a hypercubic box t l the infinite cylinder t and the crossover regime from hypercubic to cylindrical scaling for the two phase case n 2 we find that the crossover length l is given by o lw exp lv where is the inverse temperature is the surface tension and w 1 2 if v 1 2 whilew 0 if v 1 2 for the standard ising model we also consider free boundary conditions showing that l exp lv o lv 1 for any dimension v 1 2 for v 1 2 we finally discuss a class of boundary conditions which interpolate between free corresponding to the interpolating parameter g 0 and periodic boundary conditions corresponding to g 1 finding that l o lw exp lv withw 0 forg 0 andw 1 2 for 0 g 1

hardy littlewood sobolev inequalities for a class of non symmetric and non doubling hypoelliptic semigroups in his seminal 1934 paper on brownian motion and the theory of gases kolmogorov introduced a second order evolution equation which displays some challenging features in the opening of his 1967 hypoellipticity paper hormander discussed a general class of degenerate ornstein uhlenbeck operators that includes kolmogorov s as a special case in this note we combine semigroup theory with a nonlocal calculus for these hypoelliptic operators to establish new inequalities of hardy littlewood sobolev type in the situation when the drift matrix has nonnegative trace our work has been influenced by ideas of e stein and varopoulos in the framework of symmetric semigroups one of our objectives is to show that such ideas can be pushed to successfully handle the present degenerate non symmetric setting

a simple gauss newton procedure for covariance structure analysis with high level computer languages an implementation of the gauss newton algorithm for the analysis of covariance structures that is specifically adapted for high level computer languages is reviewed with this procedure one need only describe the structural form of the population covariance matrix and provide a sample covariance matrix and initial values for the parameters the gradient and approximate hessian which vary from model to model are computed numerically using this approach the entire method can be operationalized in a comparatively small program a large class of models can be estimated including many that utilize functional relationships among the parameters that are not possible in most available computer programs some examples are provided to illustrate how the algorithm can be used

finite size analysis of two dimensional u 1 lattice gauge theories we analyse the finite size scaling of two dimensional u 1 lattice gauge theories with a theta term interaction the finite size corrections to the specific heat binder landau and u4 cumulants agree with the expected asymptotic behaviour for first order phase transitions however we find that the leading correction to the position of the extremal points of these quantities is not universal on the other hand the finite size corrections to the mass gap behave as for second order phase transitions in particular the curves corresponding to different size approximations do not cross in the vicinity of the transition points the feature is associated to the existence of a divergent correlation length and holds for a wider class of models

nonconvergence improper solutions and starting values in lisrel maximum likelihood estimation in the framework of a robustness study on maximum likelihood estimation with lisrel three types of problems are dealt with nonconvergence improper solutions and choice of starting values the purpose of the paper is to illustrate why and to what extent these problems are of importance for users of lisrel the ways in which these issues may affect the design and conclusions of robustness research is also discussed

tight bounds for mixing of the swendsen wang algorithm at the potts transition point we study two widely used algorithms for the potts model on rectangular subsets of the hypercubic lattice mathbb z d heat bath dynamics and the swendsen wang algorithm and prove that under certain circumstances the mixing in these algorithms is torpid or slow in particular we show that for heat bath dynamics throughout the region of phase coexistence and for the swendsen wang algorithm at the transition point the mixing time in a box of side length l with periodic boundary conditions has upper and lower bounds which are exponential in ld 1 this work provides the first upper bound of this form for the swendsen wang algorithm and gives lower bounds for both algorithms which significantly improve the previous lower bounds that were exponential in l log l 2

the direct product model for the mtmm matrix parameterized as a second order factor analysis model the composite direct product model for the multitrait multimethod matrix is reparameterized as a second order factor analysis model this facilitates the use of widely available computer programs such as lisrel and liscomp for fitting the model

finite size scaling and surface tension from effective one dimensional systems we develop a method for precise asymptotic analysis of partition functions near first order phase transitions working in a 1 dimensional cylinder of volumel l t we show that leading exponentials int can be determined from a simple matrix calculation providedt v logl through a careful surface analysis we relate the off diagonal matrix elements of this matrix to the surface tension andl while the diagonal matrix elements of this matrix are related to the metastable free energies of the model for the off diagonal matrix elements which are related to the crossover length from hypercubic l t to cylindrical t scaling this includes a determination of the pre exponential power ofl as a function of dimension the results are applied to supersymmetric field theory and in a forthcoming paper to the finite size scaling of the magnetization and inner energy at field and temperature driven first order transitions in the crossover region from hypercubic to cylindrical scaling

more tricks of the trade reparameterizing lisrel models using negative variances this paper shows how lisrel may be used to estimate simplex models which impose constraints on the variances of endogenous variables this technique allows us to estimate both the parameters and the standard errors of the correlated measurement error model proposed by wiley and wiley 1974

a new proof of moser s parabolic harnack inequality using the old ideas of nash in 1958 nash published his fundamental work on the local holder continuity of solutions of second order parabolic equations with coefficients which need not be smooth 8 the primary purpose of that work was to study the properties of the fundamental solution corresponding to the parabolic operator and from these properties to derive regularity for a general solution though the work is often cited in the literature about weak solutions of elliptic and parabolic equations one feels that nash s ideas were never fully understood and maybe still are not and that because of this the more understandable and seemingly more fruitful ideas of de giorgi 4 and moser 6 7 were subsequently adopted

critical phenomena with convergent series expansions in a finite volume linked cluster expansions are generalized from an infinite to a finite volume they are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase a new criterion is proposed to distinguish first from second order transitions within a finite size scaling analysis the criterion applies also to other methods for investigating the phase structure such as monte carlo simulations our computational tools are illustrated with the example of scalar o n models with four and six point couplings forn 1 andn 4 in three dimensions it is shown how to localize the tricritical line in these models we indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity

covariance structure analysis in several populations this paper is concerned with the study of covariance structural models in several populations estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach asymptotic properties of the constrained estimator are studied and asymptotic chi square tests are presented to evaluate appropriate model comparisons the method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates the methodology is demonstrated by a set of real data

level sets of the fundamental solution and harnack inequality for degenerate equations of kolmogorov type in this paper we establish a uniform harnack inequality for a class of degenerate equations whose prototype is kolmogorov s equations in r3 dyyu ydzu dtu o our approach is based on mean value formulas for solutions of the equation under consideration on the level sets of the fundamental solution

on the relationship between item response theory and factor analysis of discretized variables equivalence of marginal likelihood of the two parameter normal ogive model in item response theory irt and factor analysis of dichotomized variables fa was formally proved the basic result on the dichotomous variables was extended to multicategory cases both ordered and unordered categorical data pair comparison data arising from multiple judgment sampling were discussed as a special case of the unordered categorical data a taxonomy of data for the irt and fa models was also attempted

interfaces in the potts model i pirogov sinai theory of the fortuin kasteleyn representation we develop a new analysis of the order disorder transition in ferromagnetic potts models for large numberq of spin states we use the pirogov sinai theory which we adapt to the fortuin kasteleyn representation of the models this theory applies in a rather direct way in our approach and leads to a system of non interacting contours with small activities as a consequence simpler and more natural techniques are found allowing us to recover previous results on the bulk properties of the model which then extend to non integer values ofq and to deal with non translation invariant boundary conditions this will be applied in a second part of this work to study the behaviour of the interfaces at the transition point

finite size scaling for first order phase transitions rigorous results abstract recent rigorous results on finite size effects for lattice models are reviewed we consider symmetric and asymmetric first order phase transitions in cubic and cylindrical geometries and discuss the determination of transition points from finite size data

identification of inconsistent variates in factor analysis when some of observed variates do not conform to the model under consideration they will have a serious effect on the results of statistical analysis in factor analysis the model with inconsistent variates may result in improper solutions in this article a useful method for identifying a variate as inconsistent is proposed in factor analysis the procedure is based on the likelihood principle several statistical properties such as the effect of misspecified hypotheses the problem of multiple comparisons and robustness to violation of distributional assumptions are investigated the procedure is illustrated by some examples

a unified approach to phase diagrams in field theory and statistical mechanics we construct the phase diagram of any system which admits a low temperature polymer or cluster expansion such an expansion turns the system into a hard core interacting contour model with small but not necessarily positive activities the method uses some of zahradnik s ideas z1 but applies equally well to systems with complex interactions we give two applications first to low temperaturep 2 models with complex couplings and second to a computation of asymptotics of partition functions in periodic volumes if the index of a supersymmetric field theory is known the second application would help determine the number of phases in infinite volume

parameterizing inequality constraints on unique variances in linear structural models current computer programs for analyzing linear structural models will apparently handle only two types of constraints fixed parameters and equality of parameters an important constraint not handled is inequality this is particularly crucial for preventing negative variance estimates in this paper a method is described for imposing several kinds of inequality constraints in models without the necessity for having computer programs which explicitly allow such constraints the examples discussed include the prevention of heywood cases extension to inequalities of parameters to be greater than a specified value and imposing ordered inequalities

curvature terms in small time heat kernel expansion for a model class of hypoelliptic hormander operators we consider the heat equation associated with a class of second order hypoelliptic h o rmander operators with constant second order term and linear drift we describe the possible small time heat kernel expansion on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature like invariants of the optimal control problem associated with the diffusion operator

harnack inequality for a class of kolmogorov fokker planck equations in non divergence form we prove invariant harnack inequalities for certain classes of non divergence form equations of kolmogorov type the operators we consider exhibit invariance properties with respect to a homogeneous lie group structure the coefficient matrix is assumed either to satisfy a cordes landis condition on the eigenvalues or to admit a uniform modulus of continuity

surface induced finite size effects for first order phase transitions we consider classical lattice models describing first order phase transitions and study the finite size scaling of the magnetization and susceptibility in order to model the effects of an actual surface in systems such as small magnetic clusters we consider models with free boundary conditions for a field driven transition with two coexisting phases at the infinite volume transition pointh h t we prove that the low temperature finite volume magnetizationmfree l h per site in a cubic volume of sizel d behaves like m free l h frac m m 2 frac m m 2 tanh left frac m m 2 l d h h chi l right o left frac 1 l right whereh x l is the position of the maximum of the finite volume susceptibility andm are the infinite volume magnetizations ath h t 0 andh h t 0 respectively we show thath x l is shifted by an amount proportional to 1 l with respect to the infinite volume transition pointh t provided the surface free energies of the two phases at the transition point are different this should be compared with the shift for periodic boundary conditions which for an asymmetric transition with two coexisting phases is proportional only to 1 l2d one can consider also other definitions of finite volume transition points for example the positionh u l of the maximum of the so called binder cumulantufree l h whileh u l is again shifted by an amount proportional to 1 l with respect to the infinite volume transition pointh t its shift with respect toh l is of the much smaller order 1 l2d we give explicit formulas for the proportionality factors and show that in the leading 1 l2d term the relative shift is the same as that for periodic boundary conditions