double scaling limit for matrix models with nonanalytic potentials we study the double scaling limit for unitary invariant ensembles of random matrices with nonanalytic potentials and find the asymptotic expansion for the entries of the corresponding jacobi matrix our approach is based on the perturbation expansion for the string equations the first order perturbation terms of the jacobi matrix coefficients are expressed through the hastings mcleod solution of the painleve ii equation the limiting reproducing kernel is expressed in terms of solutions of the dirac system of differential equations with a potential defined by the first order terms of the expansion

universality at the edge of the spectrum for unitary orthogonal and symplectic ensembles of random matrices we prove universality at the edge of the spectrum for unitary 2 orthogonal 1 and symplectic 4 ensembles of random matrices in the scaling limit for a class of weights w x e v x where v is a polynomial v x 2mx2m 2m 0 the precise statement of our results is given in theorem 1 1 and corollaries 1 2 and 1 4 below for the same class of weights a proof of universality in the bulk of the spectrum is given in 12 for the unitary ensembles and in 9 for the orthogonal and symplectic ensembles our starting point in the unitary case is 12 and for the orthogonal and symplectic cases we rely on our recent work 9 which in turn depends on the earlier work of widom 46 and tracy and widom 42 as in 9 the uniform plancherel rotach type asymptotics for the orthogonal polynomials found in 12 plays a central role the formulae in 46 express the correlation kernels for 1 4 as a sum of a christoffel darboux cd term as in the case 2 together with a correction term in the bulk scaling limit 9 the correction term is of lower order and does not contribute to the limiting form of the correlation kernel by contrast in the edge scaling limit considered here the cd term and the correction term contribute to the same order this leads to additional technical difficulties over and above 49 2006 wiley periodicals inc

revealed preference tests for weak separability an integer programming approach we present the revealed preference conditions that characterize the data sets that are consistent with the maximization of a weakly separable utility function we show that verifying these revealed preference conditions is np hard we also present an integer programming approach which is particularly attractive in view of empirical analysis we demonstrate the versatility of this integer programming approach by showing that it allows for testing homothetic separability and weak separability of the indirect utility function we illustrate the practical usefulness of the approach by an empirical application to spanish household consumption data

level spacings distribution for large random matrices gaussian fluctuations we study the level spacings distribution for eigenvalues of large n x n matrices from the classical compact groups in the scaling limit when the mean distance between nearest eigenvalues equals 1 defining by 77n s the number of nearest neighbors spacings greater than s 0 smaller than s 0 we prove functional limit theorem for the process 77n s e n s n1 2 giving weak convergence of this distribution to some gaussian random process on 0 x the limiting gaussian random process is universal for all classical compact groups it is holder continuous with any exponent less than 1 2 similar results can be obtained for the n level spacings distribution

move based heuristics for the unidirectional loop network layout problem we consider the loop network layout problem in a manufacturing system where n machines must be placed in n available locations around a loop to minimize the total flow distance the formulation of the problem results in a quadratic assignment problem which is computationally a very hard problem we discuss the idea of positional moves and local improvement algorithms based on moves or k way particularly 2 way interchanges even though the concept of moves has not found its way into algorithmic design in the existing literature our computational experimentation with two move based heuristics indicates uniformly superior performance in comparison to the well known pairwise interchange heuristic

estimation of nonparametric models with simultaneity we introduce methods for estimating nonparametric nonadditive models with simultaneity the methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables such as ratios of derivatives or averages of products of derivatives of this density the estimators are therefore easily computed functionals of a nonparametric estimator of the density of the observable variables we consider in detail a model where to each structural equation there corresponds an exclusive regressor and a model with one equation of interest and one instrument that is included in a second equation for both models we provide new characterizations of observational equivalence on a set in terms of the density of the observable variables and derivatives of the structural functions based on those characterizations we develop two estimation methods in the first method the estimators of the structural derivatives are calculated by a simple matrix inversion and matrix multiplication analogous to a standard least squares estimator but with the elements of the matrices being averages of products of derivatives of nonparametric density estimators in the second method the estimators of the structural derivatives are calculated in two steps in a first step values of the instrument are found at which the density of the observable variables satisfies some properties in the second step the estimators are calculated directly from the values of derivatives of the density of the observable variables evaluated at the found values of the instrument we show that both pointwise estimators are consistent and asymptotically normal

universality properties of gelfand tsetlin patterns a standard gelfand tsetlin pattern of depth n is a configuration of particles in 1 ldots n times mathbb r for each r in 1 ldots n r times mathbb r is referred to as the rth level of the pattern a standard gelfand tsetlin pattern has exactly r particles on each level r and particles on adjacent levels satisfy an interlacing constraint probability distributions on the set of gelfand tsetlin patterns of depth n arise naturally as distributions of eigenvalue minor processes of random hermitian matrices of size n we consider such probability spaces when the distribution of the matrix is unitarily invariant prove a determinantal structure for a broad subclass and calculate the correlation kernel in particular we consider the case where the eigenvalues of the random matrix are fixed this corresponds to choosing uniformly from the set of gelfand tsetlin patterns whose nth level is fixed at the eigenvalues of the matrix fixing q n in 1 ldots n and letting n under the assumption that frac q n n to alpha in 0 1 and the empirical distribution of the particles on the nth level converges weakly the asymptotic behaviour of particles on level q n is relevant to free probability theory saddle point analysis is used to identify the set in which these particles behave asymptotically like a determinantal random point field with the sine kernel

instrumental variable estimation of nonseparable models there are many environments where knowledge of a structural relationship is required to answer questions of interest also nonseparability of a structural disturbance is a key feature of many models here we consider nonparametric identification and estimation of a model that is monotonic in a nonseparable scalar disturbance which disturbance is independent of instruments this model leads to conditional quantile restrictions we give local identification conditions for the structural equations from those quantile restrictions we find that a modified completeness condition is sufficient for local identification we also consider estimation via a nonparametric minimum distance estimator the estimator minimizes the sum of squares of predicted values from a nonparametric regression of the quantile residual on the instruments we show consistency of this estimator

bounds for best response functions in binary games abstract this paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs the best response function gives the utility maximizing response to a decision of the other players this is analogous to the response function in the treatment response literature taking the decision of the other players as the treatment except that the best response function has additional structure implied by the associated utility maximization problem further the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment response literature we focus especially on the case of a complete information entry game with two firms we also discuss the case of an entry game with many firms non entry games and incomplete information our analysis of the entry game is based on the observation of realized entry decisions which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms including the assumption of nash equilibrium play the symmetry of the payoffs between firms and whether mixed strategies are admitted

bounding quantile demand functions using revealed preference inequalities this paper develops a new technique for the estimation of consumer demand models with unobserved heterogeneity subject to revealed preference inequality restrictions particular attention is given to nonseparable heterogeneity the inequality restrictions are used to identify bounds on quantile demand functions a nonparametric estimator for these bounds is developed and asymptotic properties are derived an empirical application using data from the u k family expenditure survey illustrates the usefulness of the methods by deriving bounds and con dence sets for estimated quantile demand functions

the identification problem in systems nonlinear in the variables this paper examines the identifiability of the coefficients of a single equation in a simultaneous equation model which is nonlinear only in the variables the concept of identifiability in this model is motivated and developed using the closely related concept of observational equivalence this framework is then utilized to develop necessary and sufficient conditions for identifiability when the disturbances are required to be independent of the exogenous variables the approach recommended by fisher is shown to yield sufficient but not necessary conditions for identifiability for several relatively common special cases the necessary and sufficient conditions are found to simplify to the familiar rank condition for identifiability in the linear model the simultaneous equation model that is nonlinear only in the variables has enjoyed widespread application in economics such models are linear in the parameters and typically seem to be linear in the variables as well when viewing a single equation in many models the nonlinearity in the variables arises due to endogenous variables entering in different forms in different equations logged and unlogged form for example in macroeconometric models nonlinearity in the variables arises when the model includes endogenous real nominal and price variables which are nonlinearly related 2 whatever the reason for the nonlinearity in the variables it is important to determine the conditions under which the equations of such models can be identified

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

transport maps for beta matrix models and universality we construct approximate transport maps for non critical beta matrix models that is maps so that the push forward of a non critical beta matrix model with a given potential is a non critical beta matrix model with another potential up to a small error in the total variation distance one of the main features of our construction is that these maps enjoy regularity estimates that are uniform in the dimension in addition we find a very useful asymptotic expansion for such maps which allows us to deduce that local statistics have the same asymptotic behavior for both models

on the nonparametric identification of nonlinear simultaneous equations models comment on brown 1983 and roehrig 1988 this note revisits the identification theorems of brown 1983 and roehrig 1988 we describe an error in the proofs of the main identification theorems in these papers and provide an important counterexample to the theorems on the identification of the reduced form specifically the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions of these papers we provide conditions under which the reduced form is identified and is recoverable using the distribution of the endogenous variables conditional on the exogenous variables however these conditions place substantial limitations on the structural model we conclude the note with a conjecture that it may be possible to use classical exclusion restrictions to recover some of the key implications of the theorems in more general settings

conditions for identification in nonparametric and parametric models on presente une definition formelle de l identification dans un contexte non parametrique sur la base des travaux de koopmans et reiersol 1950

gaussian fluctuation for the number of particles in airy bessel sine and other determinantal random point fields we prove the central limit theorem clt for the number of eigenvalues near the spectrum edge for certain hermitian ensembles of random matrices to derive our results we use a general theorem essentially due to costin and lebowitz concerning the gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions as another corollary of the costin lebowitz theorem we prove the clt for the empirical distribution function of the eigenvalues of random matrices from classical compact groups

generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields the equilibrium measure in the presence of an external field plays a role in a number of areas in analysis for example in random matrix theory the limiting mean density of eigenvalues is precisely the density of the equilibrium measure typical behavior for the equilibrium measure is 1 it is positive on the interior of a finite number of intervals 2 it vanishes like a square root at endpoints and 3 outside the support there is strict inequality in the euler lagrange variational conditions if these conditions hold then the limiting local eigenvalue statistics is loosely described by a bulk in which there is universal behavior involving the sine kernel and edge effects in which there is a universal behavior involving the airy kernel through techniques from potential theory and integrable systems we show that this regular behavior is generic for equilibrium measures associated with real analytic external fields in particular we show that for any one parameter family of external fields v c the equilibrium measure exhibits this regular behavior except for an at most countable number of values of c we discuss applications of our results to random matrices orthogonal polynomials and integrable systems 2000 john wiley sons inc

on independence conditions in nonseparable models observable and unobservable instruments this paper develops identification results employing independence conditions among unobservable variables the independence conditions are used to derive first stage nonseparable reduced form functions once constructed these reduced form functions are employed to express the derivatives of nonseparable structural functions in terms of the derivatives of the reduced form functions for models with simultaneity we obtain the new results by combining the independence assumptions together with parametric specifications and exclusion restrictions for models with triangularity we allow all functions to be nonparametric and nonseparable in unobservable random terms for the latter we provide several equivalence results and discuss some of the trade offs between observable and unobservable instruments

asymptotics of skew orthogonal polynomials exact integral expressions of the skew orthogonal polynomials involved in orthogonal 1 and symplectic 4 random matrix ensembles are obtained the even rank skew orthogonal polynomials are average characteristic polynomials of random matrices from there asymptotics of the skew orthogonal polynomials are derived

limiting laws of linear eigenvalue statistics for hermitian matrix models we study the variance and the laplace transform of the probability law of linear eigenvalue statistics of unitary invariant matrix models of n n hermitian matrices as n assuming that the test function of statistics is smooth enough and using the asymptotic formulas by deift et al commun pure appl math 52 1325 1425 1999 for orthogonal polynomials with varying weights we show first that if the support of the density of states of the model consists of q 2 intervals then in the global regime the variance of statistics is a quasiperiodic function of n as n generically in the potential determining the model we show next that the exponent of the laplace transform of the probability law is not in general 1 2 variance as it should be if the central limit theorem would be valid and we find the asymptotic form of the laplace transform of the probability law in certain cases

identification in nonparametric simultaneous equations models this paper provides conditions for identification of functionals in nonparametric simultaneous equations models with nonadditive unobservable random terms the conditions are derived from a characterization of observational equivalence between models we show that in the models considered observational equivalence can be characterized by a restriction on the rank of a matrix the use of the new results is exemplified by deriving previously known results about identification in parametric and nonparametric models as well as new results a stylized method for analyzing identification which is useful in some situations is also presented

on universality of local edge regime for the deformed gaussian unitary ensemble we consider the deformed gaussian ensemble h n h n 0 m n in which h n 0 is a hermitian matrix possibly random and m n is the gaussian unitary random matrix gue independent of h n 0 assuming that the normalized counting measure of h n 0 converges weakly in probability if random to a non random measure n 0 with a bounded support and assuming some conditions on the convergence rate we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of h n

double scaling limit in the random matrix model the riemann hilbert approach we prove the existence of the double scaling limit in the unitary matrix model with quartic interaction and we show that the correlation functions in the double scaling limit are expressed in terms of the integrable kernel determined by the function for the hastings mcleod solution to the painleve ii equation the proof is based on the riemann hilbert approach and the central point of the proof is an analysis of analytic semiclassical asymptotics for the function at the critical point in the presence of four coalescing turning points 2003 wiley periodicals inc

universality at the edge of the spectrum in wigner random matrices we prove universality at the edge for rescaled correlation functions of wigner random matrices in the limit n as a corollary we show that after proper rescaling the 1th 2nd 3rd etc eigenvalues of wigner random hermitian resp real symmetric matrix weakly converge to the distributions established by tracy and widom in g u e g o e cases

on the statistical mechanics approach in the random matrix theory integrated density of states we consider the ensemble of random symmetricn n matrices specified by an orthogonal invariant probability distribution we treat this distribution as a gibbs measure of a mean field type model this allows us to show that the normalized eigenvalue counting function of this ensemble converges in probability to a nonrandom limit asn and that this limiting distribution is the solution of a certain self consistent equation

universality of general beta ensembles we prove the universality of the ensembles with convex analytic potentials and for any 0 i e we show that the spacing distributions of log gases at any inverse temperature coincide with those of the gaussian ensembles

bulk eigenvalue statistics for random regular graphs ak was partly supported by swiss national science foundation grant 144662 hty was partly supported by nsf grant dms 1307444 and a simons investigator fellowship

spectral properties of random reactance networks and random matrix pencils our goal is to study the statistical properies of dielectric resonances which are poles of conductance of a large random lc network such poles are a particular example of eigenvalues n of matrix pencils h w with w being a positive definite matrix and h a random real symmetric one we first consider spectra of the matrix pencils with independent identically distributed entries of h then we concentrate on an infinite range full connectivity version of a random lc network in all cases we calculate the mean eigenvalue density and the two point correlation function in the framework of efetov s supersymmetry approach fluctuations in spectra turn out to be the same as those provided by the wigner dyson theory of usual random matrices

polyhedral structure and properties of a model for layout design abstract in flexible manufacturing systems the type of materials handling system strongly influences the machine layout this paper studies the problem of determining a machine layout for uni directional loop networks which minimizes the maximum number of loop traversals for a family of parts which we show to be np complete we also show that the polyhedral structure of its integer programming formulation is closely related to that of the maximum weight acyclic subgraph problem we introduce inequalities that define facets and faces of the convex hull of solutions for the layout problem which also define corresponding facets and faces for the acyclic subgraph polytope preliminary computational results are also presented

dummy endogenous variables in weakly separable models in this paper we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term the model is not required to be strictly increasing in the error term and the class of models considered includes limited dependent variable models such as discrete choice models conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions

on universality for orthogonal ensembles of random matrices we prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum our starting point is the tracy widom formula for the matrix reproducing kernel the key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive toeplitz matrix and a two diagonal skew symmetric toeplitz matrix

universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles this paper is devoted to the rigorous proof of the universality conjecture of random matrix theory according to which the limiting eigenvalue statistics ofn n random matrices within spectral intervals ofo n 1 is determined by the type of matrix real symmetric hermitian or quaternion real and by the density of states we prove this conjecture for a certain class of the hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function the potential in the quantum field theory satisfying some regularity conditions

identification in nonseparable models weak nonparametric restrictions are developed sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable these derivatives can exhibit stochastic variation in a microeconometric context this allows the impact of a policy intervention as measured by the value of a structural derivative to vary across people who are identical as measured by covariates when the restrictions are satisfied quantiles of the distribution of a policy impact across people can be identified the identification restrictions are local in the sense that they are specific to the values of the covariates and the specific quantiles of latent variables at which identification is sought the conditions do not include the commonly required independence of latent variables and covariates they include local versions of the classical rank and order conditions and local quantile insensitivity conditions values of structural derivatives are identified by functionals of quantile regression functions and can be estimated using the same functionals applied to estimated quantile regression functions

nonparametric estimation of nonadditive random functions we present estimators for nonparametric functions that are nonadditive in unobservable random terms the distributions of the unobservable random terms are assumed to be unknown we show that when a nonadditive nonparametric function is strictly monotone in an unobservable random term and it satisfies some other properties that may be implied by economic theory such as homogeneity of degree one or separability the function and the distribution of the unobservable random term are identified we also present convenient normalizations to use when the properties of the function other than strict monotonicity in the unobservable random term are unknown the estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal we extend the results to functions that depend on a multivariate random term the results of a limited simulation study are presented

nonparametric instrumental regression the focus of this paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions that stem from a structural econometric model e y f z w 0 and involve endogenous variables y and z and instruments w the function f is the solution of an ill posed inverse problem and we propose an estimation procedure based on tikhonov regularization the paper analyzes identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function

tracy widom distributions in critical unitary random matrix ensembles and the coupled painleve ii system we study fredholm determinants of the painleve ii and painleve xxxiv kernels in certain critical unitary random matrix ensembles these determinants describe special gap probabilities of eigenvalues we obtain tracy widom formulas for the fredholm determinants which are explicitly given in terms of integrals involving a family of distinguished solutions to the coupled painleve ii system in dimension four moreover the large gap asymptotics for these fredholm determinants are derived where the constant terms are given explicitly in terms of the riemann zeta function

nonparametric identification of the distribution of random coefficients in binary response static games of complete information this paper studies binary response static games of complete information allowing complex heterogeneity through a random coefficients specification the main result of the paper establishes nonparametric point identification of the joint density of all random coefficients except those on interaction effects under additional independence assumptions we identify the joint density of the interaction coefficients moreover we prove that in the presence of covariates that are common to both players the player specific coefficient densities are identified while the joint density of all random coefficients is not point identified however we do provide bounds on counterfactual probabilities that involve this joint density

universality of a double scaling limit near singular edge points in random matrix models we consider unitary random matrix ensembles z n s t 1 e n tr v s t m dm on the space of hermitian n n matrices m where the confining potential vs t is such that the limiting mean density of eigenvalues as n and s t 0 vanishes like a power 5 2 at a singular endpoint of its support the main purpose of this paper is to prove universality of the eigenvalue correlation kernel in a double scaling limit the limiting kernel is built out of functions associated with a special solution of the pi2 equation which is a fourth order analogue of the painleve i equation in order to prove our result we use the well known connection between the eigenvalue correlation kernel and the riemann hilbert rh problem for orthogonal polynomials together with the deift zhou steepest descent method to analyze the rh problem asymptotically the key step in the asymptotic analysis will be the construction of a parametrix near the singular endpoint for which we use the model rh problem for the special solution of the pi2 equation

on the acyclic subgraph polytope the acyclic subgraph problem can be formulated as follows given a digraph with arc weights find a set of arcs containing no directed cycle and having maximum total weight we investigate this problem from a polyhedral point of view and determine several classes of facets for the associated acyclic subgraph polytope we also show that the separation problem for the facet defining dicycle inequalities can be solved in polynomial time this implies that the acyclic subgraph problem can be solved in polynomial time for weakly acyclic digraphs this generalizes a result of lucchesi for planar digraphs

semiclassical asymptotics of orthogonal polynomials riemann hilbert problem and universality in the matrix model we derive semiclassical asymptotics for the orthogonal polynomials pn z on the line with respect to the exponential weight exp inv z where v z is a double well quartic polynomial in the limit when n n 1 we assume that n n cri for some 0 where cr is the critical value which separates orthogonal polynomials with two cuts from the ones with one cut simultaneously we derive semiclassical asymptotics for the recursive coe cients of the orthogonal polynomials and we show that these coe cients form a cycle of period two which drifts slowly with the change of the ratio n n the proof of the semiclassical asymptotics is based on the methods of the theory of integrable systems and on the analysis of the appropriate matrix riemannhilbert problem as an application of the semiclassical asymptotics of the orthogonal polynomials we prove the universality of the local distribution of eigenvalues in the matrix model with the double well quartic interaction in the presence of two cuts contents

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

fluctuations of matrix elements of regular functions of gaussian random matrices we find the limit of the variance and prove the central limit theorem clt for the matrix elements jk m j k 1 n of a regular function of the gaussian matrix m goe and gue as its size n tends to infinity we show that unlike the linear eigenvalue statistics tr m a traditional object of random matrix theory whose variance is bounded as n and the clt is valid for tr m e tr m the variance of jk m is o 1 n and the clt is valid for sqrt n varphi jk m mathbf e varphi jk m this shows the role of eigenvectors in the forming of the asymptotic regime of various functions statistics of random matrices our proof is based on the use of the fourier transform as a basic characteristic function unlike the stieltjes transform and moments used in majority of works of the field we also comment on the validity of analogous results for other random matrices

displacement convexity for the generalized orthogonal ensemble the generalized orthogonal ensemble of n n real symmetric matrices x has probability measure nu n left dx right z n 1 exp left ntracev left x right right where dx is the product of lebesgue measure on the matrix entries and v left x right geqslant left 2 delta right log left x right with 0 the eigenvalue distribution is concentrated on left a mathord left vphantom a 2 right kern nulldelimiterspace 2 a mathord left vphantom a 2 right kern nulldelimiterspace 2 right for some a 0 or if the variance of the trace is o 1 n2 then the empirical distribution of eigenvalues converges weakly almost surely to some non random probability measure on a 2 a 2 as o left sqrt log n mathord left vphantom n n 2 right kern nulldelimiterspace n 2 right these conditions are satisfied for certain polynomial potentials the logarithmic energy is displacement convex as a functional on charge distributions with fixed mean along the real line when the trace distribution satisfies a logarithmic sobolev inequality or equivalently a quadratic transportation inequality the joint eigenvalue distributions and the limiting equilibrium measure likewise satisfy quadratic transportation inequalities in the sense of talagrand 24

on the largest eigenvalue of a random subgraph of the hypercube let g be a random subgraph of the n cube where each edge appears randomly and independently with probability p we prove that the largest eigenvalue of the adjacency matrix of g is almost surely lambda 1 g 1 o 1 max delta 1 2 g n p where g is the maximum degree of g and the o 1 term tends to zero as max 1 2 g np tends to infinity

limit correlation functions for fixed trace random matrix ensembles universal limits for the eigenvalue correlation functions in the bulk of the spectrum are shown for a class of nondeterminantal random matrices known as the fixed trace or the hilbert schmidt ensemble these universal limits have been proved before for determinantal hermitian matrix ensembles and for some special classes of the wigner random matrices

orthogonal polynomials with respect to varying weights in this paper we review a connection of orthogonal polynomials with respect to varying weights to weighted approximation multipoint pade approximation and to some questions of theoretical physics

identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity we extend the identification results for nonparametric simultaneous equations models in matzkin 2008 to situations where the observations on the vector of dependent variables might be limited and where the number of exogenous unobservable variables is larger than the number of dependent variables

a graph theoretic heuristic for designing loop layout manufacturing systems abstract in flexible manufacturing systems the type of materials handling system strongly influence the machine layout for layouts where the machines are arranged in a loop and the material handling system is uni directional a measure of congestion for a part is the number of times the part traverses the loop before its processing is completed this paper investigates the problem of determining a machine layout for uni directional loop networks which minimizes the maximum number of loop traversals for a family of parts based on graph theoretic arguments a heuristic is developed which constructs a layout from a solution to the linear programming relaxation of the problem preliminary computational results are also presented

smooth coefficient estimation of a seemingly unrelated regression abstract this paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model we discuss the imposition of cross equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection a test of correct functional form for the entire system of equations is also constructed asymptotic and finite sample results are given we illustrate our estimator by applying it to a cost system for us commercial banks our results show that most of the banks are operating under increasing returns to scale but that returns to scale decrease with bank size

universality of the local spacing distribution in certain ensembles of hermitian wigner matrices consider an n n hermitian random matrix with independent entries not necessarily gaussian a so called wigner matrix it has been conjectured that the local spacing distribution i e the distribution of the distance between nearest neighbour eigenvalues in some part of the spectrum is in the limit as n the same as that of hermitian random matrices from gue we prove this conjecture for a certain subclass of hermitian wigner matrices