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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 ...
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作者：Birge, Lucien
作者单位：Sorbonne Universite
摘要：We consider here estimation of an unknown probability density belonging to where is a probability measure. We have at hand i.i.d. observations with density and use the squared -norm as our loss function. The purpose of this paper is to provide an abstract but completely general method for estimating by model selection, allowing to handle arbitrary families of finite-dimensional (possibly non-linear) models and any . We shall, in particular, consider the cases of unbounded densities and bounded...
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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...
