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作者：Ioffe, Dmitry; Velenik, Yvan
作者单位：Technion Israel Institute of Technology; University of Geneva
摘要：We consider a model of a polymer in Z(d+1), constrained to join 0 and a hyperplane at distance N. The polymer is subject to a quenched nonnegative random environment. Alternatively, the model describes crossing random walks in a random potential (see Zerner [Ann Appl. Probab. 8 (1998) 246-280] or Chapter 5 of Sznitman [Brownian Motion, Obstacles and Random Media (1998) Springer] for the original Brownian motion formulation). It was recently shown [Ann. Probab. 36 (2008) 1528-1583; Probab. Theo...
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作者：Haas, Benedicte; Miermont, Gregory
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay
摘要：We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers that determine how the size of a tree is distributed in its different subtrees. Under some natural assumption on these distributions, s...
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作者：Alsmeyer, Gerold; Biggins, J. D.; Meiners, Matthias
作者单位：University of Munster; University of Sheffield; Uppsala University
摘要：Given a sequence T = (T-i)(i >= 1) of nonnegative random variables, a function f on the positive halfline can be transformed to E Pi(i >= 1) f (tT(i)). We study the fixed points of this transform within the class of decreasing functions. By exploiting the intimate relationship with general branching processes, a full description of the set of solutions is established without the moment conditions that figure in earlier studies. Since the class of functions under consideration contains all Lapl...
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作者：Hairer, Martin; Maas, Jan
作者单位：University of Warwick; University of Bonn
摘要：We consider a class of stochastic PDEs of Burgers type in spatial dimension 1, driven by space-time white noise. Even though it is well known that these equations are well posed, it turns out that if one performs a spatial discretization of the nonlinearity in the wrong way, then the sequence of approximate equations does converge to a limit, but this limit exhibits an additional correction term. This correction term is proportional to the local quadratic cross-variation (in space) of the grad...
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作者：Menshikov, Mikhail; Popov, Serguei; Ramirez, Alejandro F.; Vachkovskaia, Marina
作者单位：Durham University; Universidade Estadual de Campinas; Pontificia Universidad Catolica de Chile
摘要：In this paper we study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86-92] by Benjamini and Wilson. We consider a discrete-time stochastic process (X-n, n = 0, 1, 2, ...) taking values on Z(d), d >= 2, described as follows: when the particle visits a site for the first time, it has a uniformly-positive drift in a given direction l; when the particle is at a site which was already visited before, it has zero drift. Assuming u...
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作者：O'Connell, Neil
作者单位：University of Warwick
摘要：We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence.
