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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.
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作者：Le Gall, JF; Le Jan, Y
作者单位：Sorbonne Universite; Universite Paris Saclay
摘要：The main idea of the present work is to associate with a general continuous branching process an exploration process that contains the desirable information about the genealogical structure. The exploration process appears as a simple local time functional of a Levy process with no negative jumps, whose Laplace exponent coincides with the branching mechanism function. This new relation between spectrally positive Levy processes and continuous branching processes provides a unified perspective ...
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作者：Brown, KS; Diaconis, P
作者单位：Cornell University; Cornell University
摘要：Let E be the set of chambers of a real hyperplane arrangement. We study a random walk on E introduced by Bidigare, Hanlon and Rockmore. This includes various shuffling schemes used in computer science, biology and card games. It also includes random walks on zonotopes and zonotopal tilings. We find the stationary distributions of these Markov chains, give good bounds on the rate of convergence to stationarity, and prove that the transition matrices are diagonalizable. The results are extended ...
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作者：Freidlin, M; Weber, M
作者单位：University System of Maryland; University of Maryland College Park; Technische Universitat Dresden
摘要：Degenerate white noise perturbations of Hamiltonian systems in R-2 are studied. In particular perturbations of a nonlinear oscillator with 1 degree of freedom are considered. If the oscillator has more than one stable equilibrium, the long time behavior of the system is defined by a diffusion process on a graph. Inside the edges the process is defined by a standard averaging procedure, but to define the process for all t > 0, one should add gluing conditions at the vertices. Calculation of the...
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作者：Piterbarg, VV
作者单位：University of Southern California
摘要：A sequence of piecewise constant approximations to rescaled isotropic homeomorphic stochastic flows is shown to converge weakly in Skorohod metric to the coalescing Brownian flow. Intermittent behavior of isotropic flows is exposed, and the clustering properties of isotropic flows are studied by the means of this convergence. We obtain qualitative and quantitative description of expansions and contractions of an arbitrary isotropic homeomorphic flow on large time- and space-scales.
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作者：Bai, ZD; Silverstein, JW
作者单位：National University of Singapore; North Carolina State University
摘要：Let B-n = (1/N)T-n(1/2) XnXn*T-n(1/2), where X-n is n x N with i.i.d, complex standardized entries having finite fourth moment and T(n)1/2 is a Hermitian square root of the nonnegative definite Hermitian matrix T-n. It is known that, as n --> infinity, if n/N converges to a positive number and the empirical distribution of the eigenvalues of T-n converges to a proper probability distribution, then the empirical distribution of the eigenvalues of B-n converges a.s. to a nonrandom limit. In this...
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作者：Giraitis, L; Taqqu, MS
作者单位：Boston University
摘要：We establish the central limit theorem for quadratic forms Sigma(t, s=1)(N) b(t-s)P-m,P- n(X-t, X-s) of the bivariate Appell polynomials P-m,P- n(X-t, X-s) under time-domain conditions. These conditions relate the weights b(t) and the covariances of the sequences (P-m,P- n(X-t, X-s)) and (X-t). The time-domain approach, together with the spectral domain approach developed earlier, yields a general set of conditions for central limit theorems.
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作者：Hu, YY; Shi, Z
作者单位：Sorbonne Universite; Sorbonne Universite
摘要：We study the sample path asymptotics of a class of recurrent diffusion processes with random potentials, including examples of Sinai's simple random walk in random environment and Brox's diffusion process with Brownian potential. The main results consist of several integral criteria which completely characterize all the possible Levy classes, therefore providing a very precise image of the almost sure asymptotic behaviors of these processes.
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作者：Pitman, J; Yor, M
作者单位：University of California System; University of California Berkeley; Sorbonne Universite
摘要：An identity in distribution due to Knight for Brownian motion is extended in two different ways: first by replacing the supremum of a reflecting Brownian motion by the range of an unreflected Brownian motion and second by replacing the reflecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excursions. The first extension is related to two different constructions of Ito's law of Brownian excursions...
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作者：Haggstrom, O; Mossel, E
作者单位：Chalmers University of Technology; Hebrew University of Jerusalem
摘要：A few years ago, Grimmett, Resten and Zhang proved that for supercritical bond percolation on Z(3), simple random walk on the infinite cluster is a.s. transient. We generalize this result to a class of wedges in Z(3) including, for any epsilon is an element of (0, 1), the wedge W-epsilon = {(x, y, z) is an element of Z(3): x greater than or equal to 0, \z\ less than or equal to x(epsilon)} which can be thought of as representing a (2 + epsilon)-dimensional lattice, Our proof builds on recent w...
