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作者：Berkes, Istvan; Liu, Weidong; Wu, Wei Biao
作者单位：Graz University of Technology; Shanghai Jiao Tong University; University of Chicago
摘要：The celebrated results of Komlos, Major and Tusnady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a powerful tool in probability and statistics. In this paper we extend KMT approximation for a large class of dependent stationary processes, solving a long standing open problem in probability theory. Under the framework of stationary causal processes and functi...
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作者：Dirksen, Sjoerd
作者单位：University of Bonn
摘要：Motivated by the study of existence, uniqueness and regularity of solutions to stochastic partial differential equations driven by jump noise, we prove Ito isomorphisms for L-p-valued stochastic integrals with respect to a compensated Poisson random measure. The principal ingredients for the proof are novel Rosenthal type inequalities for independent random variables taking values in a (noncommutative) L-p-space, which may be of independent interest. As a by-product of our proof, we observe so...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a sigma-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a Levy-Ito representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.
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作者：Adler, Robert J.; Moldavskaya, Elina; Samorodnitsky, Gennady
作者单位：Technion Israel Institute of Technology; Cornell University
摘要：The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more points which lie in an excursion set belong to the same connected component has constantly eluded analysis. We study this problem from the point of view of large deviations, finding the asymptotic probabilities that two such points are connected by a path laying within the excursion set, and so belong...
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作者：Auffinger, Antonio; Damron, Michael
作者单位：University of Chicago; Princeton University
摘要：In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663-697] proved a long standing conjecture that relates the transversal exponent and the fluctuation exponent x in first-passage percolation on Z(d). The purpose of this paper is to replace the main argument of Chatterjee (2013) and give an alternative proof of this relation. Specifically, we show that under the assumption that exponents defined in Chatterjee (2013) exist, one has the relation x <= 2 xi - 1. One advantage ...
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作者：Meerschaert, Mark M.; Straka, Peter
作者单位：Michigan State University; University of New South Wales Sydney
摘要：Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their finite-dimensional distributions is an important open problem. This paper develops a general semi-Markov theory for CTRW limit processes in R-d with infinitely many particle jumps (renewals) in finite time intervals. The particle jumps and waiting times can ...
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作者：Procaccia, Eviatar B.; Shellef, Eric
作者单位：University of California System; University of California Los Angeles; Weizmann Institute of Science
摘要：Let a simple random walk run inside a torus of dimension three or higher for a number of steps which is a constant proportion of the volume. We examine geometric properties of the range, the random subgraph induced by the set of vertices visited by the walk. Distance and mixing bounds for the typical range are proven that are a k-iterated log factor from those on the full torus for arbitrary k. The proof uses hierarchical renormalization and techniques that can possibly be applied to other ran...
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作者：Sidorova, Nadia; Twarowski, Aleksander
作者单位：University of London; University College London
摘要：The parabolic Anderson model is the Cauchy problem for the heat equation on the integer lattice with a random potential xi. We consider the case when {xi(z) : z is an element of Z(d)} is a collection of independent identically distributed random variables with Weibull distribution with parameter 0 < gamma < 2, and we assume that the solution is initially localised in the origin. We prove that, as time goes to infinity, the solution completely localises at just one point with high probability, ...
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作者：Ding, Jian; Zeitouni, Ofer
作者单位：Stanford University; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and an estimate for the right tail up to a multiplicative constant on the law of the centered maximum.
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作者：Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin
作者单位：Hebrew University of Jerusalem; Microsoft; Stanford University
摘要：We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree distributions and, more generally, the limiting distribution of subgraphs in balls of any given radius k around a random vertex in the preferential attachment graph. We also establish the finite-volume corrections which give the approach to the limit.
