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作者：Gaudilliere, A.; Landim, C.
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an application we prove a some recurrence theorems. In particular, we show the recurrence of two-dimensional cycle random walks under a second moment condition on the winding numbers.
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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：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：Campos, David; Ramirez, Alejandro F.
作者单位：Pontificia Universidad Catolica de Chile; Universidad Costa Rica
摘要：We introduce ellipticity criteria for random walks in i.i.d. random environments under which we can extend the ballisticity conditions of Sznitman and the polynomial effective criteria of Berger, Drewitz and Ramirez originally defined for uniformly elliptic random walks. We prove under them the equivalence of Sznitman's condition with the polynomial effective criterion , for large enough. We furthermore give ellipticity criteria under which a random walk satisfying the polynomial effective cri...
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作者：Camia, Federico; Garban, Christophe; Newman, Charles M.
作者单位：Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); New York University
摘要：We prove that for the Ising model defined on the plane at the average magnetization under an external magnetic field behaves exactly like The proof, which is surprisingly simple compared to an analogous result for percolation [i.e. that on the triangular lattice (Kesten in Commun Math Phys 109(1):109-156, 1987; Smirnov and Werner in Math Res Lett 8(5-6):729-744, 2001)] relies on the GHS inequality as well as the RSW theorem for FK percolation from Duminil-Copin et al. (Commun Pure Appl Math 64...
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作者：Li, Xiang-Dong
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Fudan University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
