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作者：Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Goetze, Friedrich
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
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作者：Basdevant, Anne-Laure; Enriquez, Nathanael; Gerin, Lucas
作者单位：Universite Paris Saclay
摘要：On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1 + 1-p/2 + o(1 - p) with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process).
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作者：Salisbury, Thomas S.; Sezer, A. Deniz
作者单位：York University - Canada; University of Calgary
摘要：We condition super-Brownian motion on boundary statistics of the exit measure X-D from a bounded domain D. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure X-D. Two particular examples are: conditioning on a Poisson random measure with intensity beta X-D and conditioning on X-D itself. We find the conditional laws as h-transforms of the original SBM law using Dynkin's formulation of X-harmonic functions. We give explicit expressio...
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作者：Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre
作者单位：Brandeis University; University of Bonn
摘要：Consider a continuous time random walk in Z with independent and exponentially distributed jumps +/- 1. The model in this paper consists in an infinite number of such random walks starting from the complement of {-m, -m + 1, ... , m - 1, m} at time -t, returning to the same starting positions at time t, and conditioned not to intersect. This yields a determinantal process, whose gap probabilities are given by the Fredholm determinant of a kernel. Thus this model consists of two groups of rando...
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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...
