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作者：Rider, Brian; Waters, Patrick
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：We establish universality at the hard edge for general beta ensembles assuming that: the background potential V is a polynomial such that x -> V(x(2)) is strongly convex, beta >= 1, and the dimension-difference parameter a >= 0. The method rests on the corresponding tridiagonal matrix models, showing that their appropriate continuum scaling limit is given by the Stochastic Bessel Operator. As conjectured in Edelman and Sutton (J Stat Phys 127:1121-1165, 2007) and rigorously established in Rami...
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作者：Ding, Jian; Zhang, Fuxi
作者单位：University of Chicago; Peking University
摘要：Let {(v):vVN} be a discrete Gaussian free field in a two-dimensional box VN of side length N with Dirichlet boundary conditions. We study the Liouville first passage percolation, i.e., the shortest path metric where each vertex is given a weight of e(v) for some >0. We show that for sufficiently small but fixed >0, with probability tending to 1 as N, all geodesics between vertices of macroscopic Euclidean distances simultaneously have (the conjecturally unique) length exponent strictly larger ...
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作者：Matoussi, Anis; Possamai, Dylan; Sabbagh, Wissal
作者单位：Le Mans Universite; Columbia University; Universite Paris Saclay
摘要：In this article, we propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate the links between the 2BDSDEs and a class of parabolic fully nonlinear Stochastic PDEs. Precisely, we show that the Markovian solution of 2BDSDEs provide a probabilistic interpretation of the classical and stochastic viscosity solution of ...
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作者：Farfan, J.; Landim, C.; Tsunoda, K.
作者单位：Pontificia Universidad Catolica del Peru; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Osaka
摘要：We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical measure under the stationary state. We deduce from this result that the stationary state is concentrated on the stationary solutions of the hydrodynamic equation which are stable.
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作者：Dembo, Amir; Ding, Jian; Miller, Jason; Peres, Yuval
作者单位：Stanford University; University of Pennsylvania; University of Cambridge; Microsoft
摘要：Given a finite, connected graph G, the lamplighter chain on G is the lazy random walk X on the associated lamplighter graph G=Z2G. The mixing time of the lamplighter chain on the torus Zndis known to have a cutoff at a time asymptotic to the cover time of Zndif d=2, and to half the cover time if d3. We show that the mixing time of the lamplighter chain on Gn(a)=Zn2xZalogn has a cutoff at (a) times the cover time of Gn(a) as n, where is an explicit weakly decreasing map from (0,) onto [1/2,1). ...
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作者：Ambrosio, Luigi; Stra, Federico; Trevisan, Dario
作者单位：Scuola Normale Superiore di Pisa; University of Pisa
摘要：We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge-Ampere equation.
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作者：Benoist, T.; Fraas, M.; Pautrat, Y.; Pellegrini, C.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); KU Leuven; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices, and is then given by a random product of correlated matrices taken from the support of the defining measure. We give natural conditions on this support that imply that the Markov chain admits a unique invariant probability measure. We moreover prove the geometric convergence towards this invariant meas...
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作者：Imamura, Takashi; Sasamoto, Tomohiro
作者单位：Chiba University; Institute of Science Tokyo; Tokyo Institute of Technology
摘要：We consider the q-totally asymmetric simple exclusion process (q-TASEP) in the stationary regime and study the fluctuation of the position of a particle. We first observe that the problem can be studied as a limiting case of an N-particle q-TASEP with a random initial condition and with particle dependent hopping rate. Then we explain how this N-particle q-TASEP can be encoded in a dynamics on a two-sided Gelfand-Tsetlin cone described by a two-sided q-Whittaker process and present a Fredholm ...
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作者：Huang, Jiaoyang; Landon, Benjamin
作者单位：Harvard University
摘要：We study Dyson Brownian motion with general potential V and for general beta >= 1. For short times t = o(1) and under suitable conditions on V we obtain a local law and corresponding rigidity estimates on the particle locations; that is, with overwhelming probability, the particles are close to their classical locations with an almost-optimal error estimate. Under the condition that the density of states of the initial data is bounded below and above down to the scale eta(*) << t << 1, we prov...
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作者：Che, Ziliang; Landon, Benjamin
作者单位：Harvard University
摘要：We consider the local statistics of H = V * XV + U * YU where V and U are independent Haar-distributed unitary matrices, and X and Y are deterministic real diagonal matrices. In the bulk, we prove that the gap statistics and correlation functions coincide with the GUE in the limit when the matrix size N -> infinity under mild assumptions on X and certain rigidity assumptions on Y (the latter being an assumption on the convergence of the eigenvalues of Y to the quantiles of its limiting spectra...
