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作者：Shi, Z
作者单位：Sorbonne Universite
摘要：We are interested in the almost sure asymptotic behavior of the windings of planar Brownian motion. Both the usual lim sup and Chung's lim inf versions of the law of the iterated logarithm are presented for the so-called big and small winding angles. Our method is based on some very accurate estimates of the winding clock. The corresponding problem for a spherically symmetric random walk in R-2 is also studied. A strong approximation using the Brownian big winding process is established. Simil...
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作者：Janvresse, E
作者单位：Universite de Rouen Normandie
摘要：The hydrodynamic limit of the symmetric simple exclusion process with speed change is given by a diffusive equation in the appropriate scale. Following the nongradient method introduced by Varadhan and the Navier-Stokes methods developed by Yau, we prove that in the same scale, the next order correction is given by a third order equation for dimension d greater than or equal to 3.
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作者：Lee, TY; Yau, HT
作者单位：University System of Maryland; University of Maryland College Park; New York University
摘要：We determine the logarithmic Sobolev constant for the Bernoulli-Laplace model and the time to stationarity for the symmetric simple exclusion model up to the leading order. Our method for proving the logarithmic Sobolev inequality is based on a martingale approach and is applied to the random transposition model as well. The proof for the time to stationarity is based on a general observation relating the time to stationarity to the hydrodynamical limit.
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作者：Adams, TM; Nobel, AB
作者单位：University System of Ohio; Ohio State University; University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider the problem of L-p-consistent density estimation from the initial segments of strongly dependent processes. It is shown that no procedure can consistently estimate the one-dimensional marginal density of every stationary ergodic process for which such a density exists. A similar result is established for the problem of estimating the support of the marginal distribution of an ergodic process.
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作者：Dhersin, JS; Le Gall, JF
作者单位：Universite Paris Cite; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We prove a Kolmogorov test for super-Brownian motion started at the Dirac mass at the origin. More precisely, we determine the functions g such that for all t small enough, the support of the process at time t will be contained in the ball of radius g(t) centered at 0. As a consequence, we get a necessary and sufficient condition for the existence in certain spacetime domains of a solution of the associated semilinear partial differential equation that blows up at the origin.
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作者：Rezakhanlou, F
作者单位：University of California System; University of California Berkeley
摘要：We study a one-dimensional particle system in which particles travel deterministically in between stochastic collisions. As the total number of particles tends to infinity, the empirical density converges to a solution of a discrete Boltzmann equation. We establish the large deviation principle for the convergence with a rate function that is given by a Variational formula. Some of the properties of the rate function are discussed and a nonvariational expression for the rate function is given.
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作者：Pradeilles, F
作者单位：Institut Polytechnique de Paris; ENSAE Paris
摘要：We first show a large deviation principle for degenerate diffusion-transmutation processes and study the Riemannian metric associated with the action functional under a Hormander-type assumption. Then we study the behavior of the solution u(epsilon) of a system of strongly coupled scaled KPP equations. Using backward stochastic differential equations and the theory of Hamilton-Jacobi equations, we show that, when the parabolic operator satisfies a Hormander-type hypothesis or when the nonlinea...
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作者：Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：The simple random walk on a supercritical Galton-Watson tree is transient when the tree is infinite. Moreover, there exist regeneration times, that is, times when the walk crosses an edge for the first and the last time. We prove that the distance and the range of the walk satisfy functional central limit theorems under the annealed law GP. This result is a consequence of estimates of the law of the first regeneration time tau(R). We show that there exist positive c, c', alpha and beta such th...
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作者：Gadidov, A
作者单位：Gannon University
摘要：Let m greater than or equal to 2 be a nonnegative integer and let {X-(l), X-i((l))}(i) (is an element of) (N), l = 1,..., m, be m independent sequences of independent and identically distributed symmetric random variables. Define S-n = Sigma(1 less than or equal to 1, ... i) (m less than or equal to n) X-i1((1)) ... X-im((m)), and let {gamma(n)}(n is an element of N) be a nondecreasing sequence of positive numbers, tending to infinity and satisfying some regularity conditions. For m = 2 necess...
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作者：Bramson, M; Cox, JT; Durrett, RR
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Syracuse University; Cornell University; Cornell University
摘要：The voter model, with mutations occurring at a positive rate alpha, has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in d greater than or equal to 2. We show that, as alpha --> 0, the limiting distribution is right triangular in d = 2 and uniform in d greater than or equal to 3. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions.
