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作者：Lytvynov, Eugene
作者单位：Swansea University
摘要：Let X be a locally compact Polish space and let in be a reference Radon measure on X. Let Gamma(X) denote the configuration space over X, that is, the space of all locally finite subsets of X. A point process on X is a probability measure on Gamma(X). A point process mu is called determinantal if its correlation functions have the form k((n)) (x(1), ... , x(n)) = det[K (x(i), x(j))](i, j=1, ... ,n). The function K(x, y) is called the correlation kernel of the determinantal point process mu. As...
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作者：Cheliotis, Dimitris; Virag, Balint
作者单位：National & Kapodistrian University of Athens; University of Toronto; University of Toronto
摘要：Sinai's random walk in random environment shows interesting patterns on the exponential time scale. We characterize the patterns that appear on infinitely many time scales after appropriate resealing (a functional law of iterated logarithm). The curious rate function captures the difference between one-sided and two-sided behavior.
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作者：Cerf, Raphael; Manzo, Francesco
作者单位：Universite Paris Saclay; Roma Tre University
摘要：This work extends to dimension d >= 3 the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on Z(d) evolving with the Metropolis dynamics under a fixed small positive magnetic field h starting from the minus phase. When the inverse temperature beta goes to infinity, the relaxation time of the system, defined as the time when the plus phase has invaded the origin, behaves like exp(beta k(d)). The value k(d) is equal to k(d) =1/d+1(Gamma(1) +...+ Gamma(d)), where G...
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作者：Fukushima, Ryoki
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：Consider a d-dimensional Brownian motion in a random potential defined by attaching a nonnegative and polynomially decaying potential around Poisson points. We introduce a repulsive interaction between the Brownian path and the Poisson points by weighting the measure by the Feynman-Kac functional. We show that under the weighted measure, the Brownian motion tends to localize around the origin. We also determine the scaling limit of the path and also the limit shape of the random potential.
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作者：Buraczewski, D.; Damek, E.; Mikosch, T.; Zienkiewicz, J.
作者单位：University of Wroclaw; University of Copenhagen
摘要：In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207-248] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise sequence of the equations can have light tails. The results of the paper are analogs to those obtained by A. V. Nagaev [Theory Probab. Appl. 14 (1969) 51-64; 193-208] and S. V....
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作者：Amini, Omid; Devroye, Luc; Griffiths, Simon; Olver, Neil
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); McGill University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Massachusetts Institute of Technology (MIT)
摘要：Consider a branching random walk on R, with offspring distribution Z and nonnegative displacement distribution W. We say that explosion occurs if an infinite number of particles may be found within a finite distance of the origin. In this paper, we investigate this phenomenon when the offspring distribution Z is heavy-tailed. Under an appropriate condition, we are able to characterize the pairs (Z, W) for which explosion occurs, by demonstrating the equivalence of explosion with a seemingly mu...
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作者：Bramson, Maury; Burdzy, Krzysztof; Kendall, Wilfrid
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle; University of Warwick
摘要：Two random processes X and Y on a metric space are said to be epsilon-shy coupled if there is positive probability of them staying at least a positive distance E apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous nonexistence results for co-adapted shy coupling of reflected Brownian motion required convexity...
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作者：Redig, Frank; Voellering, Florian
作者单位：Delft University of Technology; University of Gottingen
摘要：We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker, that is, the environment process. We can transfer the rate of mixing in time of the environment to the rate of mixing of the environment process with a loss of at most polynomial order. Therefore the method is applicable to environments with sufficiently fast...
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作者：Huesmann, Martin; Sturm, Karl-Theodor
作者单位：University of Bonn
摘要：This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson point process. We prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite. Moreover, we give precise conditions for the latter which demonstrate a sharp threshold at d = 2. The cost will be defined in terms of an arbitrary increasing function of the distance. The coupling will be realized by means of a transport map (allocation map) which assigns to e...
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作者：Anderson, Greg W.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：For polynomials in independent Wigner matrices, we prove convergence of the largest singular value to the operator norm of the corresponding polynomial in free semicircular variables, under fourth moment hypotheses. We actually prove a more general result of the form no eigenvalues outside the support of the limiting eigenvalue distribution. We build on ideas of Haagerup-Schultz-Thorbjornsen on the one hand and Bai-Silverstein on the other. We refine the linearization trick so as to preserve s...
