-
作者：Popescu, Ionel
作者单位：University System of Georgia; Georgia Institute of Technology; Institute of Mathematics of the Romanian Academy
摘要：In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given in Dumitriu and Edelman (J. Math. Phys. 43(11): 5830-5847, 2002; J. Math. Phys. 47(11):5830-5847, 2006). We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions in some particular cases. We also discuss the limit of fluctuations, which, in a general context, turn out to be Gaussian. For the case of several random matrices, we prove the co...
-
作者：Mossel, Elchanan; Weitz, Dror; Wormald, Nicholas
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Waterloo
摘要：We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity lambda, where the weight of an independent set I is lambda(|I|). A recent result has established that Gibbs sampling is rapidly mixing in sampling the distribution for graphs of maximum degree d and lambda < lambda (c) (d), where lambda (c) (d) is the critical activity for uniqueness of the Gibbs measure (i.e., for decay of correlations with distance in the weight...
-
作者：Buraczewski, Dariusz; Damek, Ewa; Guivarc'h, Yves; Hulanicki, Andrzej; Urban, Roman
作者单位：University of Wroclaw; Universite de Rennes
摘要：We consider a stochastic recursion Xn+1 = Mn+1Xn + Q(n+1), (n is an element of N), where (Q(n), M-n) are i.i.d. random variables such that Qn are translations, Mn are similarities of the Euclidean space R-d and X-n is an element of R-d. In the present paper we show that if the recursion has a unique stationary measure nu with unbounded support then the weak limit of properly dilated. exists and defines a homogeneous tail measure Lambda. The structure of Lambda is studied and the supports of nu...
-
作者：Doering, Maik; Stannat, Wilhelm
作者单位：Technical University of Darmstadt
摘要：We prove that the Dirichlet form associated with the Wasserstein diffusion on the set of all probability measures on the unit interval, introduced in von Renesse and Sturm (Entropic measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev inequality. This implies hypercontractivity of the associated transition semigroup. We also study functional inequalities for related diffusion processes.
-
作者：Bolthausen, Erwin; Funaki, Tadahisa; Otobe, Tatsushi
作者单位：University of Tokyo; University of Zurich
摘要：We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of R-d, especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the st...
-
作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in question. In this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments. In the process, we introduce a notion of 'second order Poincare inequalities': just as ordinary Poincare inequalities give variance b...
-
作者：Armendariz, Ines; Loulakis, Michail
作者单位：Universidad de San Andres Argentina; Universidade de Sao Paulo; University of Crete
摘要：We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system. We show that in the thermodynamic limit the rest of the sites have joint distribution equal to the grand canonical measure at the critical density. This improves the result of Grosskinsky, Schutz and Spohn,...
-
作者：Durand, Arnaud
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We completely describe the size and large intersection properties of the Holder singularity sets of L,vy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a L,vy process. The Holder singularity sets of the sample paths of certain random wavelet series are investigated as well.
-
作者：Jara, M. D.; Landim, C.; Sethuraman, S.
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Iowa State University
摘要：We prove a non-equilibrium functional central limit theorem for the position of a tagged particle in mean-zero one-dimensional zero-range process. The asymptotic behavior of the tagged particle is described by a stochastic differential equation governed by the solution of the hydrodynamic equation.
-
作者：Raimond, Olivier
作者单位：Universite Paris Saclay
摘要：We study asymptotic properties of processes X, living in a Riemannian compact manifold M, solution of the stochastic differential equation (SDE) dX(t) = dW(t)(X-t) - beta(t)del V mu(t)(X-t)dt with W a Brownian vector field, beta(t) = a log(t + 1), mu(t) = 1/t integral(t)(0) delta(Xs)ds and V mu(t)(x) = 1/t integral(t)(0) V(x, X-s)ds, V being a smooth function. We show that the asymptotic behavior of mu(t) can be described by a non-autonomous differential equation. This class of processes exten...
