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作者：Forrester, Peter J.; Ipsen, Jesper R.
作者单位：University of Melbourne
摘要：The zeros of the random Laurent series 1/mu - 8 j=1 c j / z j, where each c j is an independent standard complex Gaussian, is known to correspond to the scaled eigenvalues of a particular additive rank 1 perturbation of a standard complex Gaussian matrix. For the corresponding random Maclaurin series obtained by the replacement z . 1/ z, we show that these same zeros correspond to the scaled eigenvalues of a particular multiplicative rank 1 perturbation of a random unitary matrix. Since the co...
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作者：Gorin, Vadim; Rahman, Mustazee
作者单位：Massachusetts Institute of Technology (MIT); Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：This paper finds the bulk local limit of the swap process of uniformly random sorting networks. The limit object is defined through a deterministic procedure, a local version of the Edelman-Greene algorithm, applied to a two dimensional determinantal point process with explicit kernel. The latter describes the asymptotic joint law near 0 of the eigenvalues of the corners in the antisymmetric Gaussian Unitary Ensemble. In particular, the limiting law of the first time a given swap appears in a ...
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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：Berestycki, Nathanael; Sengul, Bati
作者单位：University of Cambridge
摘要：We prove a conjecture raised by the work of Diaconis and Shahshahani (Z Wahrscheinlichkeitstheorie Verwandte Geb 57(2):159-179, 1981) about the mixing time of random walks on the permutation group induced by a given conjugacy class. To do this we exploit a connection with coalescence and fragmentation processes and control the Kantorovich distance by using a variant of a coupling due to Oded Schramm as well as contractivity of the distance. Recasting our proof in the language of Ricci curvatur...
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作者：Powell, Ellen
摘要：We study branching diffusions in a bounded domain D of Rd in which particles are killed upon hitting the boundary D. It is known that any such process undergoes a phase transition when the branching rate exceeds a critical value: a multiple of the first eigenvalue of the generator of the diffusion. We investigate the system at criticality and show that the associated genealogical tree, when the process is conditioned to survive for a long time, converges to Aldous' Continuum Random Tree under ...
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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.
