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作者：Offret, Yoann
作者单位：University of Neuchatel
摘要：We consider a family of one-dimensional diffusions, in dynamical Wiener mediums, which are random perturbations of the Ornstein-Uhlenbeck diffusion process. We prove quenched and annealed convergences in distribution and under weigh-ted total variation norms. We find two kind of stationary probability measures, which are either the standard normal distribution or a quasi-invariant measure, depending on the environment, and which is naturally connected to a random dynamical system. We apply the...
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作者：Berestycki, Julien; Berestycki, Nathanael; Schweinsberg, Jason
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; University of California System; University of California San Diego
摘要：We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of -root 2. Kesten (Stoch Process 7:9-47, 1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time t. These bounds improve upon results of Kesten (Stoch Process 7:9-47, 1978), and partially confirm nonrigorous pred...
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作者：Goodman, Jesse; den Hollander, Frank
作者单位：Leiden University - Excl LUMC; Leiden University
摘要：The path of a Brownian motion on a -dimensional torus run for time is a random compact subset of . We study the geometric properties of the complement as for . In particular, we show that the largest regions in have a linear scale , where is the capacity of the unit ball. More specifically, we identify the sets for which contains a translate of , and we count the number of disjoint such translates. Furthermore, we derive large deviation principles for the largest inradius of as and the -cover ...
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作者：Denker, Manfred; Gordin, Mikhail
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University
摘要：For a measure preserving transformation of a probability space and some we investigate almost sure and distributional convergence of random variables of the form where C1,C2,...are normalizing constants and the kernel belongs to an appropriate subspace in some . We establish a form of the individual ergodic theorem for such sequences. Using a filtration compatible with and the martingale approximation, we prove a central limit theorem in the non-degenerate case; for a class of canonical (total...
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作者：Basdevant, Anne-Laure; Schapira, Bruno; Singh, Arvind
作者单位：Universite Paris Saclay; Universite Paris Saclay
摘要：We consider a vertex reinforced random walk on the integer lattice with sub-linear reinforcement. Under some assumptions on the regular variation of the weight function, we characterize whether the walk gets stuck on a finite interval. When this happens, we estimate the size of the localization set. In particular, we show that, for any odd number larger than or equal to , there exists a vertex reinforced random walk which localizes with positive probability on exactly consecutive sites.
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作者：Mikosch, Thomas; Wintenberger, Olivier
作者单位：University of Copenhagen; Universite PSL; Universite Paris-Dauphine
摘要：We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition.
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作者：Asselah, Amine; Gaudilliere, Alexandre
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider internal diffusion limited aggregation in dimension two or more. This is a random cluster growth model, where random walks start at the origin of the lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. When random walks are sent from the origin, we establish a lower bound for the inner and outer errors fluctuations of order square root of the logarithm of . When dimension is three or more, this lower bound matches the upper bound rec...
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作者：Kifer, Yuri; Rapaport, Ariel
作者单位：Hebrew University of Jerusalem
摘要：It was shown in Kifer (Israel J Math, 2013) that for any subshift of finite type considered with a Gibbs invariant measure the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of almost all points are asymptotically Poisson distributed. Here we not only extend this result to all psi-mixing shifts with countable alphabet but actually show that for all points the distributions of these numbers are asymptotically close either to Poisson or to compound Poisson distributions....
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Wang, Xuan
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Random graph models with limited choice have been studied extensively with the goal of understanding the mechanism of the emergence of the giant component. One of the standard models are the Achlioptas random graph processes on a fixed set of n vertices. Here at each step, one chooses two edges uniformly at random and then decides which one to add to the existing configuration according to some criterion. An important class of such rules are the bounded-size rules where for a fixed K >= 1, all...
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作者：Yin, Jun
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：In the first part (Bourgade et al., Local circular law for random matrices, preprint, arXiv: 1206.1449, 2012) of this article series, Bourgade, Yau and the author of this paper proved a local version of the circular law up to the finest scale N-1/2+epsilon for non-Hermitian random matrices at any point z is an element of C with parallel to z vertical bar-1 vertical bar > c for any constant c > 0 independent of the size of the matrix. In the second part (Bourgade et al., The local circular law ...
