3-4期

最新文章

• Quasi-static limit for the asymmetric simple exclusion AI翻译
  作者：De Masi, Anna; Marchesani, Stefano; Olla, Stefano; Xu, Lu
  作者单位：University of L'Aquila; Gran Sasso Science Institute (GSSI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institut Universitaire de France
  摘要：We study the one-dimensional asymmetric simple exclusion process on the lattice (1, ..., N) with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale N-a with a > 0. We prove that at the time scale N1+a the system evolves quasi-statically with a macroscopic density profile given by the entropy solution of the stationary Burgers equation with boundary densities changing in time, determined by the corresponding microscopic boundary rates....
• Accelerating abelian random walks with hyperbolic dynamics AI翻译
  作者：Dubail, Bastien; Massoulie, Laurent
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Inria; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
  摘要：Given integers d >= 2, n >= 1, we consider affine random walks on torii (Z/nZ)(d) defined as Xt+1 = AX(t) + B-t mod n, where A is an element of GL(d)(Z) is a invertible matrix with integer entries and (B-t)(t >= 0) is a sequence of iid random increments on Z(d). We show that when A has no eigenvalues of modulus 1, this random walk mixes in O (log n log log n) steps as n -> infinity, and mixes actually in O (log n) steps only for almost all n. These results are similar to those of Chung et al. ...
• Planarity and non-separating cycles in uniform high genus quadrangulations AI翻译
  作者：Louf, Baptiste
  作者单位：Uppsala University
  摘要：We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.
• Multi-point distribution of discrete time periodic TASEP AI翻译
  作者：Liao, Yuchen
  作者单位：University of Warwick
  摘要：We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial conditions. The formula involves contour integrals of Fredholm determinants with kernels acting on certain discrete spaces. For a class of initial conditions satisfying certain technical assumptions, we are able to derive large-time, large-period limit of the joint di...
• Convergence of the spectral radius of a random matrix through its characteristic polynomial AI翻译
  作者：Bordenave, Charles; Chafai, Djalil; Garcia-Zelada, David
  作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine
  摘要：Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in probability. This result can also be seen as the convergence of the support in the circular law theorem under optimal moment conditions. In the proof we establish the convergence in law of the reciprocal characteristic polynomial to a random analytic function...
• Gaussian unitary ensemble in random lozenge tilings AI翻译
  作者：Aggarwal, Amol; Gorin, Vadim
  作者单位：Columbia University; University of California System; University of California Berkeley
  摘要：This paper establishes a universality result for scaling limits of uniformly random lozenge tilings of large domains. We prove that whenever the boundary of the domain has three adjacent straight segments inclined under 120 degrees (measured in the direction internal to the domain) to each other, the asymptotics of tilings near the middle segment is described by the GUE-corners process of random matrix theory. An important step in our argument is to show that fluctuations of the height functio...
• The local limit of uniform spanning trees AI翻译
  作者：Nachmias, Asaf; Peres, Yuval
  作者单位：Tel Aviv University; University System of Ohio; Kent State University; Kent State University Kent; Kent State University Salem
  摘要：We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to infinity is the Poisson(1) branching process conditioned to survive forever. An extension to almost regular graphs and a quenched version are also given.
• Cutoff profiles for quantum Levy processes and quantum random transpositions AI翻译
  作者：Freslon, Amaury; Teyssier, Lucas; Wang, Simeng
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of Vienna; Harbin Institute of Technology
  摘要：We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time N ln(N). Then, we study the induced classical process on the real line and compute its atoms and density. This enables us to find the cutoff profile, which involves free Poisson distributions and the semicircle law. We prove similar results for quantum permutations and quantum random transpositions.
• Grassmannian stochastic analysis and the stochastic quantization of Euclidean fermions AI翻译
  作者：Albeverio, Sergio; Borasi, Luigi; De Vecchi, Francesco C.; Gubinelli, Massimiliano
  作者单位：University of Bonn
  摘要：We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum probability: a Grassmann random variable is an homomorphism of an abstract Grassmann algebra into a quantum probability space, i.e. a C*-algebra endowed with a suitable state. We define the notion of Gaussian processes, Brownian motion and stochastic (partial) d...
• Number of paths in oriented percolation as zero temperature limit of directed polymer AI翻译
  作者：Fukushima, Ryoki; Junk, Stefan
  作者单位：University of Tsukuba; Tohoku University
  摘要：We prove that the free energy of directed polymer in Bernoulli environment converges to the growth rate for the number of open paths in super-critical oriented percolation as the temperature tends to zero. Our proof is based on rate of convergence results which hold uniformly in the temperature. We also prove that the convergence rate is locally uniform in the percolation parameter inside the super-critical phase, which implies that the growth rate depends continuously on the percolation param...