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作者：Kortchemski, Igor
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaym,-Galton-Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.
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作者：Miller, Jason; Sousi, Perla
作者单位：University of Cambridge
摘要：Suppose that X is a simple random walk on for and, for each t, we let consist of those which have not been visited by X by time t. Let be the expected amount of time that it takes for X to visit every site of . We show that there exists and a time as such that the following is true. For (resp. ), the total variation distance between the law of and the law of i.i.d. Bernoulli random variables indexed by with success probability tends to 0 (resp. 1) as . Let be the first time t that . We also sh...
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作者：Lewicka, Marta; Manfredi, Juan J.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We present a probabilistic approach to the obstacle problem for the p-Laplace operator. The solutions are approximated by running processes determined by tug-of-war games plus noise, and letting the step size go to zero, not unlike the case when Brownian motion is approximated by random walks. Rather than stopping the process when the boundary is reached, the value function is obtained by maximizing over all possible stopping times that are smaller than the exit time of the domain.
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作者：Rodriguez, Pierre-Francois
作者单位：University of California System; University of California Los Angeles
摘要：We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height h. The dependence present in the model is a notorious impediment when trying to analyze the behavior near criticality. Alongside the critical threshold for percolation, a second parameter characterizes a strongly subcritical regime. We prove that the relevant crossing probabilities converge to 1 p...
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作者：Barraquand, Guillaume; Corwin, Ivan
作者单位：Columbia University; Sorbonne Universite; Universite Paris Cite; Sorbonne Universite
摘要：We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in which performs nearest neighbour jumps with transition probabilities drawn according to the Beta distribution. We also describe a related directed polymer model, which is a limit of the q-Hahn interacting particle system. Using a Fredholm determinant representation for the quenched probability distribution function of the walker's position, we are able to prove secon...
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作者：Hoi Nguyen; Tao, Terence; Van Vu
作者单位：University System of Ohio; Ohio State University; University of California System; University of California Los Angeles; Yale University
摘要：Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for random matrices with discrete entries and the first super-polynomial bound on the probability that a random graph has simple spectrum, along with several applications.
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作者：Pinsky, Ross G.; Travers, Nicholas F.
作者单位：Technion Israel Institute of Technology; Indiana University System; Indiana University Bloomington
摘要：We study a random walk on which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, p and q. R consecutive right jumps from a site in the q-mode are required to switch it to the p-mode, and L consecutive left jumps from a site in the p-mode are required to switch it to the q-mode. From a site in the p-mode the walk jumps right with probability p and left with probability , while from a site in the q-mode these probabilities are q and ...
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作者：Yogeshwaran, D.; Subag, Eliran; Adler, Robert J.
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Weizmann Institute of Science; Technion Israel Institute of Technology
摘要：We consider the topology of simplicial complexes with vertices the points of a random point process and faces determined by distance relationships between the vertices. In particular, we study the Betti numbers of these complexes as the number of vertices becomes large, obtaining limit theorems for means, strong laws, concentration inequalities and central limit theorems. As opposed to most prior papers treating random complexes, the limit with which we work is in the so-called 'thermodynamic'...
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作者：Banerjee, Sayan; Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：Maximal couplings are (probabilistic) couplings of Markov processes such that the tail probabilities of the coupling time attain the total variation lower bound (Aldous bound) uniformly for all time. Markovian (or immersion) couplings are couplings defined by strategies where neither process is allowed to look into the future of the other before making the next transition. Markovian couplings are typically easier to construct and analyze than general couplings, and play an important role in ma...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider random interlacements on Z(d), d >= 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of large side-length from the boundary of a larger homothetic box. As a corollary, we obtain an asymptotic upper bound on a similar quantity, where the random interlacements are replaced by the simple random walk. It is plausible, but open at the moment, that these asymptotic upper bo...
