-
作者：Hao, Chenxu; Li, Xinyi; Okada, Izumi; Zheng, Yushu
作者单位：Peking University; University of Tokyo; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS
摘要：On the trace of a discrete-time simple random walk on Zd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}<^>d$$\end{document} for d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{u...
-
作者：Monmarche, Pierre; Reygner, Julien
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：Non-linear versions of log-Sobolev inequalities, that link a free energy to its dissipation along the corresponding Wasserstein gradient flow (i.e. corresponds to Polyak-Lojasiewicz inequalities in this context), are known to provide global exponential long-time convergence to the free energy minimizers, and have been shown to hold in various contexts. However they cannot hold when the free energy admits critical points which are not global minimizers, which is for instance the case of the gra...
-
作者：Enriquez, Nathanael; Liu, Mike; Menard, Laurent; Perchet, Vianney
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the limiting tree. For this purpose, we introduce and study unimodular matchings on weighted unimodular random trees as well as a notion of optimality for these objects. In this context, we prove that, in law, there is a unique optimal unimodular matching for a give...
-
作者：He, Yukun
作者单位：Fudan University
摘要：Let A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} be the adjacency matrix of the Erd & odblac;s-R & eacute;nyi directed graph G(N,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mat...
-
作者：Chen, Yilin; Fehrman, Benjamin; Xu, Weijun
作者单位：Peking University; Louisiana State University System; Louisiana State University; Westlake University
摘要：We consider the periodic homogenisation problem for the generalised parabolic Anderson model on the two dimensional torus. We show that, for the renormalisation that respects Wick ordering, the homogenisation and renormalisation procedures commute. The main novelty is to identify a suitable solution ansatz beyond the usual para-controlled ansatz to set up a fixed point problem uniform in the homogenisation parameter. After that, one further utilises cancellations and resonances from the homoge...
-
作者：Hip, Andres A. Contreras; Gwynne, Ewain
作者单位：University of Chicago
摘要：We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we study asymptotics for the discrete curvature of & varepsilon;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength...
-
作者：Van Werde, Alexander; Sanders, Jaron
作者单位：Eindhoven University of Technology; University of Munster
摘要：We prove that a sum of random matrices generated by a psi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-mixing Markov chain has similar spectral properties to a Gaussian matrix with the same mean and covariance structure. This nonasymptotic universality principle enables sharp concentration i...
-
作者：Bernardin, Cedric; Chhaibi, Reda; Najnudel, Joseph; Pellegrini, Clement
作者单位：HSE University (National Research University Higher School of Economics); Communaute d'universites et etablissements de Toulouse (Comue); Universite de Toulouse (EPE); Centre National de la Recherche Scientifique (CNRS); Institut National des Sciences Appliquees de Toulouse; CNRS - National Institute for Mathematical Sciences (INSMI); University of Bristol
摘要：We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347-369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of the authors show the appearance of spikes in the filtered process, akin to a metastability phenomenon. This paper is aimed at understanding the ...
-
作者：Butori, Federico; Flandoli, Franco; Luongo, Eliseo; Tahraoui, Yassine
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld
摘要：In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly converge to the solutions of deterministic equations with a diffusion term. In the background of these stochastic models, we introduce stochastic Vlasov equations which give additional information on the fluctuations and oscillations of solutions: we prove co...
-
作者：Asselah, Amine; Schapira, Bruno; Sousi, Perla
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge
摘要：We consider branching random walks on the Euclidean lattice mostly in dimensions five and higher. In this non-Markovian setting, we derive upper bounds for the probability of spending a fixed time in each ball of an arbitrary finite collection of balls. These bounds involve the branching capacity introduced by Zhu (On the critical branching random walk I: branching capacity and visiting probability, arXiv:1611.10324). For random walks, the analogous tail estimates have been instrumental in tac...
