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作者：Dunlap, Alexander; Gu, Yu; Ryzhik, Lenya; Zeitouni, Ofer
作者单位：Stanford University; Carnegie Mellon University; Weizmann Institute of Science
摘要：We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in d >= 3 with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of Magnen and Unterberger (J Stat Phys 171:543-598, 2018).
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作者：Holmes, Mark; Perkins, Edwin
作者单位：University of Melbourne; University of British Columbia
摘要：We investigate the scaling limit of the range (the set of visited vertices) for a general class of critical lattice models, starting from a single initial particle at the origin. Conditions are given on the random sets and an associated ancestral relation under which, conditional on longterm survival, the rescaled ranges converge weakly to the range of super-Brownian motion as random sets. These hypotheses also give precise asymptotics for the limiting behaviour of the probability of exiting a...
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作者：Paindaveine, Davy; Verdebout, Thomas
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
摘要：We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction theta of a Fisher-von Mises-Langevin distribution on the p-dimensional unit hypersphere is equal to a given direction theta 0. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension pn goes to infinity at an arbitrary rate with the sample size n...
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作者：Backhoff-Veraguas, Julio; Bartl, Daniel; Beiglboeck, Mathias; Eder, Manu
作者单位：University of Vienna
摘要：A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion-Nadal and Talay i...
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作者：Addario-Berry, L.; Cairns, H.; Devroye, L.; Kerriou, C.; Mitchell, R.
作者单位：McGill University; Cornell University; McGill University
摘要：We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable (Pemantle's Min-Plus Binary Tree, 2017.[math.PR]), and to the critical random hierarchical lattice studied by Hambly and Jordan (Adv Appl Probab 36(3):824-838, 2004. 10.1239/aap/1093962236). We prove distributional convergence for the processes, after rescaling,...
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作者：Bahadoran, C.; Mountford, T.; Ravishankar, K.; Saada, E.
作者单位：Universite Clermont Auvergne (UCA); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; New York University; NYU Shanghai; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
摘要：We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process fro...
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作者：Caraceni, Alessandra; Stauffer, Alexandre
作者单位：University of Bath
摘要：We establish the first polynomial upper bound for the mixing time of random edge flips on rooted quadrangulations: we show that the spectral gap of the edge flip Markov chain on quadrangulations with n faces admits, up to constants, an upper bound of n(-5/4) and a lower bound of n(-11/2). In order to obtain the lower bound, we also consider a very natural Markov chain on plane trees-or, equivalently, on Dyck paths-and improve the previous lower bound for its spectral gap by Shor and Movassagh.
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作者：Brzezniak, Zdzislaw; Hornung, Fabian; Weis, Lutz
作者单位：University of York - UK; Helmholtz Association; Karlsruhe Institute of Technology
摘要：We consider a stochastic nonlinear Schrodinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing Stochastic NLSE in H1 on compact manifolds and bounded domains. We construct a martingale solution using a modified Faedo-Galerkin-method based on the Littlewood-Paley-decomposition. For the 2d manifolds with bounded geometry, we use the Strichartz estimates to show the pathwise uniqueness of solutions.
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作者：Chaika, Jon; Krishnan, Arjun
作者单位：Utah System of Higher Education; University of Utah; University of Rochester
摘要：We consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice. We assume that once walks meet, they coalesce. In 2d, we classify the collective behavior of these walks under mild assumptions: they either coalesce almost surely or form bi-infinite trajectories. Bi-infinite trajectories form measure-preserving dynamical systems, have a common asymptotic direction in 2d, and possess other nice properties. We use our theory to classify the be...
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作者：Hammond, Alan; Helmuth, Tyler
作者单位：University of California System; University of California Berkeley; University of Bristol
摘要：This article is concerned with self-avoiding walks (SAW) on that are subject to a self-attraction. The attraction, which rewards instances of adjacent parallel edges, introduces difficulties that are not present in ordinary SAW. Ueltschi has shown how to overcome these difficulties for sufficiently regular infinite-range step distributions and weak self-attractions (Ueltschi in Probab Theory Relat Fields 124(2):189-203, 2002). This article considers the case of bounded step distributions. For ...
