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作者：Hilario, Marcelo; Sa, Marcos; Sanchis, Remy; Teixeira, Augusto
作者单位：Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universidade de Lisboa
摘要：In this article, we consider a variety of percolation models on randomly stretched lattices. The first model we study is constructed on the usual square grid Z(2), keeping all vertices untouched while erasing edges according to the following procedure: for every integer i, the entire column of vertical edges contained in the line {x = i} is removed independently of other columns with probability rho > 0. Similarly, for every integer j, the entire row of horizontal edges contained in the line {...
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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：Yang, Kevin
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We study a general class of nonlinear Ginzburg-Landau SPDEs in infinite volume under weak nonlinearity scaling and with non-equilibrium initial data. We derive the KPZ equation as a continuum limit of these equations. This makes rigorous the original derivation of the KPZ equation from physics [] in the full-space setting, which was a problem posed in []. Our analysis is based on a stochastic heat kernel for a linearization of said SPDEs.
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作者：Chen, Xin; Wang, Jian
作者单位：Shanghai Jiao Tong University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：Brox's diffusion is a typical one-dimensional singular diffusion, which was introduced by Brox (1986) as a continuous analogue of Sinai's random walk. In this paper, we will establish quenched heat kernel estimates for short time and annealed heat kernel estimates for large time of Brox's diffusion. The proofs are based on Brox's construction via the scale-transformation and the time-change arguments as well as the theory of resistance forms for symmetric strongly recurrent Markov processes. W...
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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...
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作者：[Anonymous]
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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...
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作者：Le Gall, Jean-Francois; Riera, Armand
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped with an intrinsic metric is still a Brownian half-plane, which is independent of the part that has been removed. This is an analog of the well-known peeling procedure for random planar maps. We also investigate several distributional properties of hulls centered at a boundary point, and we provide a new construction ...
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作者：Ang, Morris; Holden, Nina; Sun, Xin; Yu, Pu
作者单位：University of California System; University of California San Diego; New York University; Peking University
摘要：Two-pointed quantum disks with a weight parameter W > 0 is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We prove that the conformal welding of the forested variant of this disk gives a two-pointed quantum disk with an independent SLE kappa for kappa is an element of (4, 8). Furthermore, we show that the conformal welding of multiple forested quantum disks gives a surface arising in Liouville conformal field theory decorated by multiple SLE kappa for kappa i...
