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作者：Bose, Arup; Hazra, Rajat Subhra; Saha, Koushik
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to accommodate other joint laws. In particular, the matricial limits of symmetric circulants and reverse circulants satisfy, respectively, the classical independence and the half independence. The matricial limits of Toeplitz and Hankel matrices do not seem to submi...
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作者：Iyer, Gautam; Novikov, Alexei
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We study the dissipation mechanism of a stochastic particle system for the Burgers equation. The velocity field of the viscous Burgers and Navier-Stokes equations can be expressed as an expected value of a stochastic process based on noisy particle trajectories [Constantin and Iyer Comm. Pure Appl. Math. 3 (2008) 330-345]. In this paper we study a particle system for the viscous Burgers equations using a Monte-Carlo version of the above; we consider N copies of the above stochastic flow, each ...
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作者：Wang, Feng-Yu
作者单位：Beijing Normal University; Swansea University
摘要：By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.
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作者：Biskup, Marek; Spohn, Herbert
作者单位：University of California System; University of California Los Angeles; University of South Bohemia Ceske Budejovice; Technical University of Munich
摘要：We consider gradient fields (phi(x) : x is an element of Z(d)) whose law takes the Gibbs-Boltzmann form Z(-1) exp{-Sigma(< x,y >) V(phi(y) - phi(x))}, where the sum runs over nearest neighbors. We assume that the potential V admits the representation V(eta) := -log integral rho(dk)exp[-1/2 kappa eta(2)], where rho is a positive measure with compact support in (0, infinity). Hence, the potential V is symmetric, but nonconvex in general. While for strictly convex V's, the translation-invariant, ...
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作者：Sly, Allan
作者单位：Microsoft
摘要：The reconstruction problem on the tree has been studied in numerous contexts including statistical physics, information theory and computational biology. However, rigorous reconstruction thresholds have only been established in a small number of models. We prove the first exact reconstruction threshold in a nonbinary model establishing the Kesten-Stigum bound for the 3-state Potts model on regular trees of large degree. We further establish that the Kesten-Stigum bound is not tight for the q-s...
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作者：Goldenshluger, Alexander; Lepski, Oleg
作者单位：University of Haifa; Aix-Marseille Universite
摘要：In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the L-s-norms of empirical and regression-type processes. Usefulness of the obtained results is illustrated by application to the processes appearing in kernel density estimation and in nonparametric estimation of regression functions.
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作者：Benjamini, Itai; Gurel-Gurevich, Ori; Schramm, Oded
作者单位：Weizmann Institute of Science; Microsoft
摘要：We construct a bounded degree graph G, such that a simple random walk on it is transient but the random walk path (i.e., the subgraph of all the edges the random walk has crossed) has only finitely many cutpoints, almost surely. We also prove that the expected number of cutpoints of any transient Markov chain is infinite. This answers two questions of James, Lyons and Peres [A Transient Markov Chain With Finitely Many Cutpoints (2007) Festschrift for David Freedman]. Additionally, we consider ...
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作者：Pardon, John
作者单位：Princeton University
摘要：We study the probability distribution of the area and the number of vertices of random polygons in a convex set K subset of R-2. The novel aspect of our approach is that it yields uniform estimates for all convex sets K subset of R-2 without imposing any regularity conditions on the boundary partial derivative K. Our main result is a central limit theorem for both the area and the number of vertices, setting a well-known conjecture in the field. We also obtain asymptotic results relating the g...
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作者：Adams, Stefan; Collevecchio, Andrea; Koenig, Wolfgang
作者单位：University of Warwick; Universita Ca Foscari Venezia; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider N bosons in a box in R-d with volume N/rho under the influence of a mutually repellent pair potential. The particle density p is an element of (0, infinity) is kept fixed. Our main result is the identification of the limiting free energy, f(beta, p), at positive temperature 1/beta, in terms of an explicit variational formula, for any fixed rho if beta is sufficiently small, and for any fixed beta if rho is sufficiently small. The thermodynamic equilibrium is described by the symmet...
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作者：Berestycki, Nathanaeel; Schramm, Oded; Zeitouni, Ofer
作者单位：University of Cambridge; Weizmann Institute of Science; University of Minnesota System; University of Minnesota Twin Cities
摘要：Let S(n) be the permutation group on n elements, and consider a random walk on S(n) whose step distribution is uniform on k-cycles. We prove a well-known conjecture that the mixing time of this process is (1/k)n log n, with threshold of width linear in n. Our proofs are elementary and purely probabilistic, and do not appeal to the representation theory of S(n).
