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作者：Jego, Antoine; Lupu, Titus; Qian, Wei
作者单位：Universite PSL; Universite Paris-Dauphine; Sorbonne Universite
摘要：We show that the occupation measure of planar Brownian motion exhibits a constant height gap of across its outer boundary. This property bears similarities with the celebrated results of Schramm-Sheffield (Schramm and Sheffield in Probab Theory Related Fields 157(1-2):47-80, 2013) and Miller-Sheffield (Miller J, Sheffield S in CLE(4) and the Gaussian free field. In preparation) concerning the height gap of 5/pi the Gaussian free field across SLE4/CLE4 curves. Heuristically, our result can also...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Ji, Hong Chang
作者单位：Institute of Science & Technology - Austria; University of Arizona; University of Wisconsin System; University of Wisconsin Madison
摘要：For general large non-Hermitian random matrices X and deterministic normal deformations A, we prove that the local eigenvalue statistics of A+X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A+X$$\end{document} close to the critical edge points of its spectrum are universal. This concludes the proof of the third an...
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作者：Banerjee, Sayan; Budhiraja, Amarjit; Imon, Dilshad
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We study a pure-jump n-particle system with attractive mean field interactions under which each particle jumps forward by a random amount, independently sampled from a given distribution theta , at exponentially distributed times with rate given by a function w of its signed distance from the system center of mass. The function w is taken to be non-increasing which leads to a 'flocking' behavior: the particles below the center of mass jump forward at a higher rate than those above it. This mod...
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作者：Kawamoto, Yosuke
作者单位：Okayama University
摘要：We consider an infinite system of interacting Brownian motions that preserves a given random point field invariant. Such dynamics are constructed using Dirichlet form theory, which naturally leads to two Dirichlet forms for the random point field: the upper and the lower Dirichlet forms. A fundamental question is the uniqueness of the Dirichlet form: that is, whether these two forms coincide. This uniqueness has often been imposed as a key assumption in the Dirichlet form approach to the stoch...
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作者：Dareiotis, Konstantinos; Holland, Teodor; Le, Khoa
作者单位：University of Leeds
摘要：We consider the stochastic reaction-diffusion equation in 1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document} dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-H & ouml;lder space with any regularity index strictly larger than -1\document...
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作者：Jirak, Moritz; Minsker, Stanislav; Shen, Yiqiu; Wahl, Martin
作者单位：University of Vienna; University of Southern California; University of Southern California; University of Bielefeld
摘要：We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the intrinsic dimensional characteristics such as the effective rank, as opposed to the dimension of the ambient space. We illustrate the advantages of such results through several applications, including new moment inequalities for sample covariance matrices and their eigenvectors w...
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作者：Haslegrave, John; Keevash, Peter
作者单位：Lancaster University; University of Oxford
摘要：We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet. We study the equilibrium time of the process, by which we mean the number of steps taken until no further interactions can occur. Under a rather general framework, we obtain high probability upper and lower bounds on the equilibrium time that match up to a c...
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作者：Ding, Jian; Wang, Jiamin
作者单位：Peking University
摘要：We study random walks in random environments generated by the two-dimensional Gaussian free field. More specifically, we consider a rescaled lattice with a small mesh size and view it as a random network where each edge is equipped with an electric resistance given by a regularization for the exponentiation of the Gaussian free field. We prove the tightness of random walks on such random networks at high temperature as the mesh size tends to 0. Our proof is based on a careful analysis of the (...
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作者：Barnes, Clayton; Mytnik, Leonid; Sun, Zhenyao
作者单位：Technion Israel Institute of Technology; Beijing Institute of Technology
摘要：Consider the [0, 1]-valued continuous random field solution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u_t(x))_{t\ge 0, x\in {\mathbb {R}}}$$\end{document} to the one-dimensional stochastic heat equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{...
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作者：Coupier, David; Dereudre, David; Gouere, Jean-Baptiste
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Lille; CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite de Tours
摘要：The state space of our model is the Euclidean space in dimension d=2. Simultaneously, from all points of a homogeneous Poisson point process, we let grow independent and identically distributed random continuum paths. Each path stops growing at time t>0 if it hits the trace of the other curves realized up until timet. Such a dynamic is well-defined as long as the distribution of paths has a finite second moment at each time t>0. Letting the time run until infinity so that each path reaches its...
