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作者：Pemantle, R; Steif, JE
作者单位：University of Wisconsin System; University of Wisconsin Madison; Chalmers University of Technology
摘要：We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d-dimensional unit sphere and the interactions are proportional to the cosines of the angles between neighboring spins. The phenomenon of interest here is the classification of phase transition (nonuniqueness of the Gibbs state) according to whether it is robust. in many cases, including all of the Heisenberg and Potts models, occurr...
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作者：Del Barrio, E; Giné, E; Matrán, C
作者单位：Universidad de Valladolid; University of Connecticut
摘要：If X is integrable, F is its cdf and F-n is the empirical cdf based on an i.i.d. sample from F, then the Wasserstein distance between F-n and F, which coincides with the L-1 norm integral(-infinity)(infinity)\F-n(t) - F(t)\ dt of the centered empirical process, tends to zero a.s. The object of this article is to obtain rates of convergence and distributional limit theorems for this law of large numbers or, equivalently, stochastic boundedness and distributional limit theorems for the L-1 norm ...
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作者：Salzano, M; Schonmann, RH
作者单位：University of California System; University of California Los Angeles
摘要：We continue the investigation of the behavior of the contact process on infinite connected graphs of bounded degree. Some questions left open by Salzano and Schonmann (1997) concerning the notions of complete convergence, partial convergence and the criterion r = s are answered. The continuity properties of the survival probability and the recurrence probability are studied. These order parameters are found to have a richer behavior than expected, with the possibility of the survival probabili...
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作者：Götze, F; Tikhomirov, AN
作者单位：University of Bielefeld; Russian Academy of Sciences; Syktyvkar State University
摘要：We consider quadratic forms [GRAPHICS] where X-j are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q(n), and the distribution of the same quadratic forms with X-j replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well. as to nonstationary AR(1) processes.
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作者：Gyöngy, I; Nualart, D
作者单位：University of Edinburgh; University of Barcelona
摘要：In this paper we establish the existence and uniqueness of an L-2(R)-valued solution for a one-dimensional Burgers' equation perturbed by a space-time white noise on the real Line. We show that the solution is continuous in space and time, provided the initial condition is continuous. The main ingredients of the proof are maximal inequalities for the stochastic convolution, and some a priori estimates far a class of deterministic parabolic equations.
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作者：Delmas, JF; Dhersin, JS
作者单位：Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Universite Paris Cite
摘要：We give a characterization of G-regularity for super-Brownian motion and the Brownian snake. More precisely, we define a capacity on E = (0, infinity) x R-d, which is not invariant by translation. We then prove that the measure of hitting a Borel set A subset of E for the graph of the Brownian snake excursion starting at (0, 0) is comparable, up to multiplicative constants, to its capacity. This implies that super-Brownian motion started at time 0 at the Dirac mass delta(0) hits immediately A ...
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作者：Millet, A; Sanz-Solé, M
作者单位：Sorbonne Universite; University of Barcelona; Universite Paris Nanterre
摘要：We prove the existence and uniqueness, for any time, of a real-valued process solving a nonlinear stochastic wave equation driven by a Gaussian noise white in time and correlated in the two-dimensional space variable. We prove that the solution is regular in the sense of the Malliavin calculus. We also give a decay condition on the covariance function of the noise under which the solution has Holder continuous trajectories and show that, under an additional ellipticity assumption, the law of t...
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作者：De Monvel, AB; Khorunzhy, A
作者单位：Sorbonne Universite; Universite Paris Cite; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We study the eigenvalue distribution of NxN symmetric random matrices H-N(x, y) = N(-1/2)h(x, y), x, y = 1,..., N, where h(x, y), x less than or equal to y are Gaussian weakly dependent random variables. We prove that the normalized eigenvalue counting function of H-N converges with probability 1 to a nonrandom function mu(lambda) as N --> infinity. We derive an equation for the Stieltjes transform of the measure d mu(lambda) and show that the latter has a compact support Lambda(mu). We find t...
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作者：Mohammed, SEA; Scheutzow, MKR
作者单位：Southern Illinois University System; Southern Illinois University; Technical University of Berlin
摘要：We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Ito-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution...
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作者：O'Brien, GL
作者单位：York University - Canada
摘要：Two classes of processes are considered. One is a class of spectrally positive infinitely divisible processes which includes all such stable processes. The other is a class of processes constructed from the sequence of partial sums of independent identically distributed positive random variables. A condition analogous to regular variation of the tails is imposed. Then a large deviation principle and a Strassen-type law of the iterated logarithm are presented. These theorems focus on unusually ...
