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作者：Barbu, Viorel; Roeckner, Michael; Russo, Francesco
作者单位：Alexandru Ioan Cuza University; University of Bielefeld; Purdue University System; Purdue University; Institut Polytechnique de Paris; ENSTA Paris
摘要：We consider a possibly degenerate porous media type equation over all of R-d with d = 1, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analyti...
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作者：Hairer, M.; Mattingly, J. C.; Scheutzow, M.
作者单位：University of Warwick; New York University; Duke University; Technical University of Berlin
摘要：There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on one hand and the existence of a spectral gap under conditions reminiscent of Harris' theorem. The first uses the existence of couplings which draw the solutions together as time goes to infinity. Such asymptotic couplings were central to (Mattingly and Sinai...
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作者：Collet, Pierre; Martinez, Servet; Meleard, Sylvie; San Martin, Jaime
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universidad de Chile; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that th...
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作者：Betz, Volker; Ueltschi, Daniel
作者单位：University of Warwick
摘要：We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certain critical density.
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作者：Addario-Berry, L.; Broutin, N.
作者单位：McGill University
摘要：We consider a branching random walk for which the maximum position of a particle in the n'th generation, R-n, has zero speed on the linear scale: R-n/n -> 0 as n -> infinity. We further remove (kill) any particle whose displacement is negative, together with its entire descendence. The size Z of the set of un-killed particles is almost surely finite (Gantert and Muller in Markov Process. Relat. Fields 12:805-814, 2006; Hu and Shi in Ann. Probab. 37(2):742-789, 2009). In this paper, we confirm ...
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作者：Ghosh, Subhankar; Goldstein, Larry
作者单位：University of Southern California
摘要：Let Y be a nonnegative random variable with mean mu and finite positive variance sigma(2), and let Y-s, defined on the same space as Y, have the Y size-biased distribution, characterized by E[Yf(Y)] = mu Ef(Y-s) for all functions f for which these expectations exist. Under a variety of conditions on Y and the coupling of Y and Ys, including combinations of boundedness and monotonicity, one sided concentration of measure inequalities such as p (Y - mu / sigma >= t) <= exp (-t(2) / 2(A + Bt) for...
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作者：Bossy, Mireille; Jabir, Jean-Francois; Talay, Denis
作者单位：Universite Cote d'Azur; Universidad de Chile
摘要：This paper is motivated by a new class of SDEs-PDEs systems, the so called Lagrangian stochastic models which are commonly used in the simulation of turbulent flows. We study a position-velocity system which is nonlinear in the sense of McKean. As the dynamics of the velocity depends on the conditional expectation with respect to its position, the interaction kernel is singular. We prove existence and uniqueness of the solution to the system by solving a nonlinear martingale problem and showin...
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作者：Mytnik, Leonid; Perkins, Edwin
作者单位：University of British Columbia; Technion Israel Institute of Technology
摘要：We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Holder continuous of index gamma > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations.
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作者：Cerf, R.; Messikh, R. J.
作者单位：Universite Paris Saclay; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the 2D-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large deviations estimates on FK-percolation events that concern the phenomenon of phase coexistence.
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作者：Damron, Michael; Sapozhnikov, Artem
作者单位：Princeton University
摘要：We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IICs). First we compute the exact decay rate of the distribution of both the weight of the kth outlet and the volume of the kth pond. Next we prove bounds for all moments of the distribution of the number of outlets in an annulus. This result leads to almost sure bounds for the number of outlets in a box B(2 (n) ) ...
