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作者：Dario, Paul
作者单位：Tel Aviv University
摘要：We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in dimension larger than 3 and have logarithmic growth in dimension 2 in the sense of stretched exponential moments. The main ingredients are a renormalization scheme of the supercritical percolation cluster, following the works of Pisztora (Probab. Theory Related Fields 104 (1996) 427-466); large-scale regularity estimates developed by Armstrong and the au...
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作者：Gravner, Janko; Holroyd, Alexander E.; Sivakoff, David
作者单位：University of California System; University of California Davis; University of Bristol; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：In the polluted bootstrap percolation model, vertices of the cubic lattice Z(3) are independently declared initially occupied with probability p or closed with probability q, where p + q <= 1. Under the standard (respectively, modified) bootstrap rule, a vertex becomes occupied at a subsequent step if it is not closed and it has at least 3 occupied neighbors (respectively, an occupied neighbor in each coordinate). We study the final density of occupied vertices as p, q -> 0. We show that this ...
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作者：Ferrari, Patrik L.; Veto, Balint
作者单位：University of Bonn; Budapest University of Technology & Economics; MTA-BME Stochastics Research Group
摘要：We consider uniform random domino tilings of the restricted Aztec diamond which is obtained by cutting off an upper triangular part of the Aztec diamond by a horizontal line. The restriction line asymptotically touches the arctic circle that is the limit shape of the north polar region in the unrestricted model. We prove that the rescaled boundary of the north polar region in the restricted domain converges to the Airy(2) process conditioned to stay below a parabola with explicit continuous st...
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作者：Last, Guenter; Nestmann, Franz; Schulte, Matthias
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Heriot Watt University
摘要：The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study first and second order properties of the numbers of components isomorphic to given finite connected graphs. For increasing observation windows in an Euclidean setting we prove qualitative multivariate and quantitative univariate central limit theorems for these ...
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作者：Hirsch, Christian; Holmes, Mark; Kleptsyn, Victor
作者单位：University of Groningen; University of Melbourne; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
摘要：We study a class of reinforcement models involving a Poisson process on the vertices of certain infinite graphs G. When a vertex fires, one of the edges incident to that vertex is selected. The edge selection is biased towards edges that have been selected many times previously, and a parameter a governs the strength of this bias. We show that for various graphs (including all graphs of bounded degree), if alpha >> 1 (the very strong reinforcement regime) then the random subgraph consisting of...
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作者：Nejjar, Peter
作者单位：University of Bonn
摘要：We consider the asymmetric simple exclusion process (ASEP) on Z with initial data such that in the large time particle density rho(.) a discontinuity (shock) at the origin is created. At the shock, the value of rho jumps from zero to one, but rho(-epsilon), 1 - rho(epsilon) > 0 for any epsilon > 0. We are interested in the rescaled position of a tagged particle which enters the shock with positive probability. We show that, inside the shock region, the particle position has the KPZ-typical 1/3...
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作者：Altmeyer, Randolf; Reiss, Markus
作者单位：Humboldt University of Berlin
摘要：The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space. For the asymptotic regime with fixed time horizon and with the spatial resolution of the observations tending to zero, we provide rate-optimal estimators and establish scaling limits of the deterministic PDE and of the SPDE on growing domains. The estimators...
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作者：Lagarias, Jeffrey C.; Rodgers, Brad
作者单位：University of Michigan System; University of Michigan; Queens University - Canada
摘要：We say that one point process on the line R mimics another at a band-width B if for each n >= 1 the two point processes have n-level correlation functions that agree when integrated against all band-limited test functions on bandwidth [-B, B]. This paper asks the question of for what values a and B can a given point process on the real line be mimicked at bandwidth B by a point process supported on the lattice aZ. For Poisson point processes we give a complete answer for allowed parameter rang...
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作者：Erhard, Dirk; Franco, Tertuliano; da Silva, Diogo S.
作者单位：Universidade Federal da Bahia
摘要：We consider the continuous time symmetric random walk with a slow bond on Z, which rates are equal to 1/2 for all bonds, except for the bond of vertices {-1, 0}, which associated rate is given by alpha n(-beta)/2, where alpha > 0 and beta is an element of [0, infinity] are the parameters of the model. We prove here a functional central limit theorem for the random walk with a slow bond: if beta is an element of [0, infinity), then it converges to the usual Brownian motion. If beta is an elemen...
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作者：Bramson, Maury; Gray, Lawrence F.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The majority vote process was one of the first interacting particle systems to be investigated. It can be described briefly as follows. There are two possible opinions at each site of a graph G. At rate 1 - epsilon, the opinion at a site aligns with the majority opinion at its neighboring sites and, at rate epsilon, the opinion at a site is randomized due to noise, where epsilon is an element of [0, 1] is a parameter. Despite the simple dynamics of the majority vote process, its equilibrium be...
