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作者：Heydenreich, Markus; van der Hofstad, Remco
作者单位：Vrije Universiteit Amsterdam; Eindhoven University of Technology
摘要：In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：We make use of the fact that a two-sided whole-plane Schramm-Loewner evolution (SLE kappa) curve gamma for kappa is an element of (0, 8) from infinity to infinity through 0 may be parametrized by its d-dimensional Minkowski content, where d = 1 + kappa/8, and become a self-similar process of index 1/d with stationary increments. We prove that such gamma is locally alpha-Holder continuous for any alpha < 1/d. In the case kappa is an element of (0, 4], we show that gamma is not locally 1/d-Holde...
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作者：Cerrai, Sandra; Freidlin, Mark
作者单位：University System of Maryland; University of Maryland College Park
摘要：Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, we introduce a new class of SPDEs defined on a graph, corresponding to the stream function of the underlying incompressible flow. We prove that, as the advection term becomes faster and faster, the solution of the stochastic reaction-diffusion-advection equation on the plane converges in a suitable sense to the solution of such an SPDE defined on the graph. ...
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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...
