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作者：Pal, Soumik; Pitman, Jim
作者单位：Cornell University; University of California System; University of California Berkeley
摘要：We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long-range behavior of the spacings between the Brownian motions arranged in increasing order. For finitely many Brownian motions interacting in this manner, we characterize drifts for which the family of laws of the vector of spacings is tight and show its convergence to a unique st...
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作者：Decreusefond, Laurent; Moyal, Pascal
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite de Technologie de Compiegne
摘要：In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/infinity. The system is represented by a point-measure valued process keeping track of the remaining processing times of the customers in service. The convergence in law of a sequence of such processes after rescaling is proved by compactness-uniqueness methods, and the deterministic fluid limit is the solution of an integrated equation in the space s' ...
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作者：van der Hofstad, Remco; Morters, Peter; Sidorova, Nadia
作者单位：Eindhoven University of Technology; University of Bath; University of London; University College London
摘要：We study the parabolic Anderson problem, that is, the heat equation partial derivative(t)u = Delta u + xi u on (0,infinity) x Z(d) with independent identically distributed random potential {xi(Z): Z is an element of Z(d)) and localized initial condition u(0, x) = 1(0)(x). Our interest is in the long-term behavior of the random total mass U(t) = Sigma(z) u (t, z) of the unique nonnegative solution in the case that the distribution of xi(0) is heavy tailed. For this, we study two paradigm cases ...
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作者：Remenik, Daniel
作者单位：Cornell University
摘要：We study a contact process running in a random environment in Z(d) where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by nonblocked sites. We give a partial description of the phase diagram of the process, showing in particular that, depending on the flip rates of the environment. survival of the contact process may or may not be possible for large values of the birth rate. We prove block cond...
