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作者：Hanen, Albert
作者单位：Universite Paris Nanterre
摘要：We study the covariance (for Gibbs measure) of spins at two sites in the case of a Sherrington-Kirkpatrick model with an external field. When the number of sites of the model grows to infinity, an asymptotic evaluation of the p moments of that covariance allows us to obtain a weak limit theorem, with a generally non-Gaussian limit law.
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作者：Merkl, Franz; Rolles, Silke W. W.
作者单位：University of Munich; Technical University of Munich
摘要：In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given by random weights on the edges. The edge weights decay exponentially in space. The process converges to a stationary process. We provide asymptotic bounds for the range of the random walker up to a given time, showing that it localizes much more than an ordi...
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作者：Hairer, M.; Ohashi, A.
作者单位：University of Warwick; Universidade Estadual de Campinas
摘要：We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a class of non-Markovian systems. They allow us to obtain a criteria for ergodicity which is similar in nature to the Doob-Khas'minskii theorem. The second part of this article shows how it is possible to apply these results to the case of stochastic different...
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作者：Balazs, M.; Rassoul-Agha, F.; Seppaelaeinen, T.; Sethuraman, S.
作者单位：Budapest University of Technology & Economics; University of Wisconsin System; University of Wisconsin Madison; Utah System of Higher Education; University of Utah; Iowa State University
摘要：We give a construction of the zero range and bricklayers' processes in the totally asymmetric, attractive case. The novelty is that we allow jump rates to grow exponentially. Earlier constructions have permitted at most linearly growing rates. We also show the invariance and extremality of a natural family of i.i.d. product measures indexed by particle density. Extremality is proved with an approach that is simpler than existing ergodicity proofs.
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作者：Yang, Ming
作者单位：Columbia University
摘要：Let X-t be any additive process in R-d. There are finite indices delta(i), beta(i), i = 1. 2 and a function u, all of which are defined in terms of the characteristics of X-t, such that lim(t -> 0) inf u(t)X--1/n(t)* = {0, if n > delta(1), {infinity, if n < delta(2), lim(t -> 0) sup u(t)X--1/n(t)* = {0, if n > beta(2), a.s., {infinity, if n < beta(1), where X-t(*) = sup(0 < s < t) |X-s|. When X-t is a Levy process with X-0 = 0, delta 1 = delta 2, beta 1 = beta 2 and u(t) = t. This is a special...
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作者：Berestycki, Julien; Berestycki, Nathanaeel; Schweinsberg, Jason
作者单位：Aix-Marseille Universite; University of California System; University of California San Diego; University of British Columbia
摘要：Coalescents with multiple collisions, also known as Lambda-coalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic coagulation in such a way that several blocks can merge at the same time to form a single block. In the case that the measure A is the Beta(2-alpha, alpha) distribution, they are also known to describe the genealogies of large populations where a single individual can produce a large number of offsprin...
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作者：Marckert, Jean-Francois; Miermont, Gregory
作者单位：Universite de Bordeaux; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Random planar maps are considered in the physics literature as the discrete counterpart of random surfaces. It is conjectured that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a limiting surface whose law does not depend, up to scaling factors, on details of the class of maps that are sampled. Previous works on the topic, starting with Chassaing and Schaeffer, have shown that the radius of a random quadrangulation with n faces, that...
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作者：van Neerven, J. M. A. M.; Veraar, M. C.; Weis, L.
作者单位：Delft University of Technology; Helmholtz Association; Karlsruhe Institute of Technology
摘要：In this paper we construct a theory of stochastic integration of processes with values in L(H, E), where H is a separable Hilbert space and E is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an H-cylindrical Brownian motion. Our approach is based on a two-sided L-p-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of L(H, E)-valued functions introduced recently by two of the...
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作者：Panchenko, Dmitry; Talagrand, Michel
作者单位：Massachusetts Institute of Technology (MIT); Sorbonne Universite; University System of Ohio; Ohio State University
摘要：In order to study certain questions concerning the distribution of the overlap in Sherrington-Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with constrained overlaps. One can write analogues of Guerra's replica symmetry breaking bound for such systems but it is not at all obvious how to choose informative functional order parameters in these bounds. We were able to make some progress for spherical pure p-sp...
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作者：Darses, Sebastien; Nourdin, Ivan
作者单位：Universite Marie et Louis Pasteur; Universite Paris Cite; Sorbonne Universite
摘要：In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given a-field Q. In our framework, we recall well-known results about Markov-Wiener diffusions. We then focus mainly on the case where X is a fractional diffusion and where 62 is the past, the future or the present of X. We treat some crucial examples and our main result is the existence of stochastic derivatives with respect to the present of X when X solves a stochastic diff...
