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作者：Peres, Yuval; Tanaka, Ryokichi; Zhai, Alex
作者单位：Tohoku University; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Stanford University
摘要：We analyze a Markov chain, known as the product replacement chain, on the set of generating n-tuples of a fixed finite group G. We show that as n. 8, the totalvariation mixing time of the chain has a cutoff at time 3 2 n log n with window of order n. This generalizes a result of Ben-Hamou and Peres (who established the result for G = Z/2) and confirms a conjecture of Diaconis and Saloff-Coste that for an arbitrary but fixed finite group, the mixing time of the product replacement chain is O(n ...
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作者：Burdzy, Krzysztof; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we consider a sequence of partitions of the edges of the metric graph with the partition size going to zero. As the mesh of the subdivision goes to zero, the conditioned random labelings converge, in a suitable sense, to a deterministic function which evolves as ...
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作者：Aru, Juhan; Lupu, Titus; Sepulveda, Avelio
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We introduce the first passage set (FPS) of constant level -a of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the boundary by a path on which the GFF does not go below -a. It is, thus, the two-dimensional analogue of the first hitting time of -a by a one-dimensional Brownian motion. We provide an axiomatic characterization of the FPS, a continuum construction using level lines, ...
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作者：Gigli, Nicola; Tamanini, Luca
作者单位：International School for Advanced Studies (SISSA); University of Bonn
摘要：In this paper we prove that, within the framework of RCD* (K, N) spaces with N < infinity, the entropic cost (i.e. the minimal value of the Schrodinger problem) admits: A threefold dynamical variational representation, in the spirit of the Benamou-Brenier formula for the Wasserstein distance; A Hamilton-Jacobi-Bellman dual representation, in line with Bobkov-Gentil-Ledoux and Otto-Villani results on the duality between Hamilton-Jacobi and continuity equation for optimal transport; A Kantorovic...
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作者：Gordina, Maria; Roeckner, Michael; Teplyaev, Alexander
作者单位：University of Connecticut; University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We consider a perturbation of a Hilbert space-valued Ornstein-Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls in the Hilbert space uniformly in time. First we introduce a new notion of generalized solutions for such equations which we call pseudo-weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation. Then ...
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作者：Gwynne, Ewain; Hutchcroft, Tom
作者单位：University of Cambridge
摘要：We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most n(1/4+on)(1) in n units of time. Together with the complementary lower bound proven by Gwynne and Miller (2017) this shows that the typical graph distance displacement of the walk after n steps is n(1/4+on) (1), as conjectured by Benjamini and Curien (Geom Funct Anal 2(2):501-531, 2013. arXiv:1202.5454). More generally, we show that the simple random walks on a cert...
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作者：Altman, Henri Elad; Zambotti, Lorenzo
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
摘要：In this article, we prove integration by parts formulae (IbPFs) for the laws of Bessel bridges from 0 to 0 over the interval [0, 1] of dimension smaller than 3. As an application, we construct a weak version of a stochastic PDE having the law of a one-dimensional Bessel bridge (i.e. the law of a reflected Brownian bridge) as reversible measure, the dimension 1 being particularly relevant in view of applications to scaling limits of dynamical critical pinning models. We also exploit the IbPFs t...
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作者：Imamura, Takashi; Mucciconi, Matteo; Sasamoto, Tomohiro
作者单位：Chiba University; Institute of Science Tokyo; Tokyo Institute of Technology
摘要：In this paper we consider the Higher Spin Six Vertex Model on the lattice Z >= 2xZ >= 1. We first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions. Exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space-time limit for the stationary Higher Spin Six Vertex Model. In particular, along the charac...
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作者：Hartarsky, Ivailo; Mareche, Laure; Toninelli, Cristina
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：Kinetically constrained models (KCM) are reversible interacting particle systems on Z(d) with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automatawith random initial state known as U-bootstrap percolation. KCM have an interest in their own right, owing to their use for modelling the liquid-glass transition in condensed matter physics. In two dimensions there are three classes of models with qualitatively different s...
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作者：Chen, Xiaohui; Kato, Kengo
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Cornell University
摘要：This paper is concerned with finite sample approximations to the supremum of a non-degenerate U-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the U-process itself is not weakly convergent as a process. Such situations arise in a variety of modern statistical problems. We first consider Gaussian approximations, namely, approximate the U-process sup...
