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作者：Eldan, Ronen
作者单位：Microsoft
摘要：We consider an analogous version of the diffusion-limited aggregation model defined on the hyperbolic plane. We prove that almost surely the aggregate viewed at time infinity will have a positive density.
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作者：Sandier, Etienne; Serfaty, Sylvia
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); New York University
摘要：We study the statistical mechanics of classical two-dimensional Coulomb gases with general potential and arbitrary beta, the inverse of the temperature. Such ensembles also correspond to random matrix models in some particular cases. The formal limit case beta = infinity corresponds to weighted Fekete sets and also falls within our analysis. It is known that in such a system points should be asymptotically distributed according to a macroscopic equilibrium measure, and that a large deviations ...
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作者：Gois, B.; Landim, C.
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the Kawasaki dynamics at inverse temperature beta for the Ising lattice gas on a two-dimensional square of length 2L + 1 with periodic boundary conditions. We assume that initially the particles form a square of length n, which may increase, as well as L, with beta. We show that in a proper time scale the particles form almost always a square and that the center of mass of the square evolves as a Brownian motion when the temperature vanishes.
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作者：Sasada, Makiko
作者单位：Keio University
摘要：We give a lower bound on the spectral gap for a class of stochastic energy exchange models. In 2011, Grigo et al. introduced the model and showed that, for a class of stochastic energy exchange models with a uniformly positive rate function, the spectral gap of an N-component system is bounded from below by a function of order N-2. In this paper, we consider the case where the rate function is not uniformly positive. For this case, the spectral gap depends not only on N but also on the average...
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作者：Kharroubi, Idris; Huyen Pham
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Institut Polytechnique de Paris; ENSAE Paris
摘要：We aim to provide a Feynman-Kac type representation for Hamilton Jacobi-Bellman equation, in terms of forward backward stochastic differential equation (FBSDE) with a simulatable forward process. For this purpose, we introduce a class of BSDE where the jumps component of the solution is subject to a partial nonpositive constraint. Existence and approximation of a unique minimal solution is proved by a penalization method under mild assumptions. We then show how minimal solution to this BSDE cl...
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作者：Khoshnevisan, Davar; Kim, Kunwoo
作者单位：Utah System of Higher Education; University of Utah
摘要：Consider the stochastic heat equation partial derivative(t)u = Lu + lambda sigma (u)xi, where L denotes the generator of a Levy process on a locally compact Hausdorff Abelian group G, sigma : R -> R is Lipschitz continuous, lambda >> 1 is a large parameter, and xi denotes space time white noise on R+ x G. The main result of this paper contains a near-dichotomy for the (expected squared) energy E(parallel to u(t)parallel to(2)(L2(G))) of the solution. Roughly speaking, that dichotomy says that,...
