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作者：Dey, Partha S.; Zygouras, Nikos
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Warwick
摘要：The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel [Ann. Probab. 42 (2014) 1212-1256]. It was proved that at inverse temperature beta n(-gamma) with gamma = 1/4 the partition function, centered appropriately, converges in distribution and the limit is given in terms of the solution of the stochastic heat equation. This result was obtained under the assumption that the disorder variables posses exponential moments, but its universality was also c...
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作者：Fournier, Nicolas; Hauray, Maxime
作者单位：Sorbonne Universite; Aix-Marseille Universite
摘要：We consider the 3D Landau equation for moderately soft potentials [gamma is an element of (-2, 0) with the usual notation] as well as a stochastic system of N particles approximating it. We first establish some strong/weak stability estimates for the Landau equation, which are fully satisfactory only when gamma is an element of [-1, 0). We next prove, under some appropriate conditions on the initial data, the so-called propagation of molecular chaos, that is, that the empirical measure of the ...
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作者：Mourrat, Jean-Christophe; Otto, Felix
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Max Planck Society
摘要：Recently, the quantification of errors in the stochastic homogenization of divergence-form operators has witnessed important progress. Our aim now is to go beyond error bounds, and give precise descriptions of the effect of the randomness, in the large-scale limit. This paper is a first step in this direction. Our main result is to identify the correlation structure of the corrector, in dimension 3 and higher. This correlation structure is similar to, but different from that of a Gaussian free...
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作者：Besalu, M.; Kohatsu-Higa, A.; Tindel, S.
作者单位：Universite de Lorraine; Universite de Lorraine; Ritsumeikan University; Japan Science & Technology Agency (JST)
摘要：In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter H. In the one-dimensional case with additive noise, our study encompasses all parameters H is an element of (0, 1), while the multidimensional case is restricted to the case H > 1/2. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.
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作者：Di Tella, Paolo; Engelbert, Hans-Juergen
作者单位：Technische Universitat Dresden; Friedrich Schiller University of Jena
摘要：In the present paper, we study the chaotic representation property for certain families X of square integrable martingales on a finite time interval [0, T]. For this purpose, we introduce the notion of compensated-covariation stability of such families. The chaotic representation property will be defined using iterated integrals with respect to a given family of square integrable martingales having deterministic mutual predictable covariation < X, Y > for all X, Y is an element of X. The main ...
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作者：Decreusefond, Laurent; Schulte, Matthias; Thaele, Christoph
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Helmholtz Association; Karlsruhe Institute of Technology; Ruhr University Bochum
摘要：A Poisson or a binomial process on an abstract state space and a symmetric function f acting on k-tuples of its points are considered. They induce a point process on the target space of f. The main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a Poisson process on the target space. The technical background are a version of Stein's method for Poisson process approximation, a Glauber dynamics representation...
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作者：Marko, Roland; Timar, Adam
作者单位：University of Bonn; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：The allocation problem for a d-dimensional Poisson point process is to find a way to partition the space to parts of equal size, and to assign the parts to the configuration points in a measurable, deterministic (equivariant) way. The goal is to make the diameter R of the part assigned to a configuration point have fast decay. We present an algorithm for d >= 3 that achieves an O(exp(- cR(d))) tail, which is optimal up to c. This improves the best previously known allocation rule, the gravitat...
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作者：Neel, Robert W.; Popescu, Ionel
作者单位：Lehigh University; University System of Georgia; Georgia Institute of Technology; Romanian Academy; Institute of Mathematics of the Romanian Academy
摘要：We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then consider geometric consequences of this stochastic representation. Based on this stochastic approach, we give a proof that, for surfaces of nonpositive Euler characteristic, the normalized Ricci flow converges to a constant curvature metric exponentially quic...
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作者：Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13
摘要：We are interested in the randomly biased random walk on the supercritical Galton-Watson tree. Our attention is focused on a slow regime when the biased random walk (X-n) is null recurrent, making a maximal displacement of order of magnitude (log n)(3) in the first n steps. We study the localization problem of X-n and prove that the quenched law of X-n can be approximated by a certain invariant probability depending on n and the random environment. As a consequence, we establish that upon the s...
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作者：Saloff-Coste, Laurent; Zheng, Tianyi
作者单位：Cornell University; Stanford University
摘要：Let G be a finitely generated group equipped with a finite symmetric generating set and the associated word length function vertical bar center dot vertical bar. We study the behavior of the probability of return for random walks driven by symmetric measures cc that are such that Sigma rho (vertical bar x vertical bar mu(x) < infinity for increasing regularly varying or slowly varying functions rho, for instance, s vertical bar -> (1 + s)(alpha), alpha is an element of(0, 2], or s vertical bar...
