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作者：Dario, Paul
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We study random surfaces with a uniformly convex gradient interaction in the presence of quenched disorder taking the form of a random independent external field. Previous work on the model has focused on proving existence and uniqueness of infinite-volume gradient Gibbs measures with a given tilt and on studying the fluctuations of the surface and its discrete gradient.In this work, we focus on the convergence of the thermodynamic limit, establishing convergence of the finite-volume distribut...
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作者：Przykucki, Michal; Roberts, Alexander; Scott, Alex
作者单位：University of Birmingham; University of Oxford
摘要：Models of parking in which cars are placed randomly and then move ac-cording to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Damron, Gravner, Junge, Lyu, and Sivakoff ((2019) Ann. Appl. Probab. 29 2089-2113) introduced a model in which cars are both placed and move at random. Independently at each point of a Cayley graph G, we place a car with probability p, and otherwise an empty parking space. Each car independently executes a random walk...
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作者：Foss, Sergey; Konstantopoulos, Takis; Pyatkin, Artem
作者单位：Heriot Watt University; University of Liverpool; Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：To each edge (i, j), i < j, of the complete directed graph on the integers we assign unit weight with probability p or weight x with probability 1 - p, independently from edge to edge, and give to each path weight equal to the sum of its edge weights. If Wx0,n is the maximum weight of all paths from 0 to n then Wx0,n/n -> Cp(x), as n -> infinity, almost surely, where Cp(x)is positive and deterministic. We study Cp(x) as a function of x, for fixed 0 < p < 1, and show that it is a strictly incre...
