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作者：Baik, Jinho; Suidan, Toufic M.
作者单位：University of Michigan System; University of Michigan; University of California System; University of California Santa Cruz
摘要：We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the mid-time behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.
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作者：Eisenbaum, Nathalie; Kaspi, Haya
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Technion Israel Institute of Technology
摘要：The problem of finding a necessary and sufficient condition for the continuity of the local times for a general Markov process is still open. Barlow and Hawkes have completely treated the case of the Levy processes, and Marcus and Rosen have solved the case of the strongly symmetric Markov processes. We treat here the continuity of the local times of Borel right processes. Our approach unifies that of Barlow and Hawkes and of Marcus and Rosen, by using an associated Gaussian process, that appe...
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作者：Kruk, Lukasz; Lehoczky, John; Ramanan, Kavita; Shreve, Steven
作者单位：Maria Curie-Sklodowska University; Carnegie Mellon University; Carnegie Mellon University
摘要：The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map Gamma(0,a) on [0,a] for any a > 0 is derived. Specifically, it is shown that on the space D[0, infinity) of right-continuous functions with left limits taking values in R, Gamma (0, a) = Lambda(a) omicron Gamma(0), where Lambda(a) : D[0, infinity) -> D [0, infinity) is defined by [Graphics] and Gamma(...
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作者：Turner, Amanda G.
作者单位：University of Cambridge
摘要：We consider sequences (X-t(N))t >= 0 of Markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form x(t) = b(x(t)), where b(x) = ((-mu)(0)(0)(lambda))x + tau(x) for some lambda, mu > 0 and tau(x) = 0(vertical bar x vertical bar(2)). Here the processes are indexed so that the variance of the fluctuations of X-t(N) is inversely proportional to N. The simplest example t arises from the OK Corral gunfight model which was formulated by ...
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作者：Kargin, Vladislav
摘要：This paper derives sufficient conditions for superconvergence of sums of bounded free random variables and provides an estimate for the rate of superconvergence.
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作者：Garet, Olivier; Marchand, Regine
作者单位：Universite de Orleans; Universite de Lorraine
摘要：The chemical distance D(x, y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behavior of this random metric, and we prove that, for an appropriate norm mu depending on the dimension and the percolation parameter, the probability of the event {0 <-> x, D(0, x)/mu(x) is not an element of (1 - epsilon, 1 + epsilon} exponentially decreases when vertical bar vertical bar x vertical bar vertical b...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We study the upper tail behaviors of the local times of the additive stable processes. Let X-1 (t),..., X-p(t) be independent, d-dimensional symmetric stable processes with stable index 0 < alpha <= 2 and consider the additive stable process (X) over bar (t(1),..., t(p)) = X-1 (t(1)) + ... + X-p (t(p)). Under the condition d < alpha p, we obtain a precise form of the large deviation principle for the local time n(x)([0, t](p)) = integral(t)(o) ... integral(t)(o) delta(x)(X-1(s(1)) + ... + X-p ...
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作者：Junge, Marius; Parcet, Javier; Xu, Quanhua
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universite Marie et Louis Pasteur
摘要：Let A denote the reduced amalgamated free product of a family A(1), A(2),..., A(n) of von Neumann algebras over a von Neumann subalgebra B with respect to normal faithful conditional expectations E-k: A(k) -> B. We investigate the norm in L-p (A) of homogeneous polynomials of a given degree d. We first generalize Voiculescu's inequality to arbitrary degree d >= 1 and indices 1 <= p <= infinity. This can be regarded as a free analogue of the classical Rosenthal inequality. Our second result is ...
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作者：Watanabe, Toshiro
作者单位：University of Aizu
摘要：A necessary and sufficient condition for the almost sure existence of an absolutely continuous (with respect to the branching measure) exact Hausdorff measure on the boundary of a Galton-Watson tree is obtained. In the case where the absolutely continuous exact Hausdorff measure does not exist almost surely, a criterion which classifies gauge functions phi according to whether pi-Hausdorff measure of the boundary minus a certain exceptional set is zero or infinity is given. Important examples ...
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作者：Kahn, Jeff; Weininger, Nicholas
摘要：A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph G obtained in two steps: first a subgraph of G is chosen according to a random cluster measure phi(p,q), and then a spin ( 1) is chosen independently for each component of the subgraph and assigned to all vertices of that component. We show that whenever q : 1, such a measure is positively associated, meaning that any two increasing events are positively correlated. This generalizes earlier ...
