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作者：Adler, M; van Moerbeke, P
作者单位：Brandeis University
摘要：In a celebrated paper, Dyson shows that the spectrum of an n x n random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n noncolliding Brownian motions held together by a drift term. The universal edge and bulk scalings for Hermitian random matrices, applied to the Dyson process, lead to the Airy and Sine processes. In particular, the Airy process is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian motion,...
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作者：Taylor, J; Takemura, A; Adler, RJ
作者单位：Stanford University; University of Tokyo; Technion Israel Institute of Technology
摘要：We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation. We also give a lower bound on this exponential rate of decay in terms of the maximal variance of a family of Gaussian processes f(x), derived...
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作者：Calka, P; Schreiber, T
作者单位：Universite Paris Cite; Nicolaus Copernicus University
摘要：In this paper, we are interested in the behavior of the typical Poisson-Voronoi cell in the plane when the radius of the largest disk centered at the nucleus and contained in the cell goes to infinity. We prove a law of large numbers for its number of vertices and the area of the cell outside the disk. Moreover, for the latter, we establish a central limit theorem as well as moderate deviation type results. The proofs deeply rely on precise connections between Poisson-Voronoi tessellations, co...
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作者：Léandre, R
作者单位：Universite Bourgogne Europe
摘要：We give two stochastic diffeologies on the free loop space which allow us to define stochastic equivariant cohomology theories in the Chen-Souriau sense and to establish a link with cyclic cohomology. With the second one, we can establish a stochastic fixed point theorem.
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作者：Einmahl, U; Deli, L
作者单位：Vrije Universiteit Brussel; Lakehead University
摘要：Let {X, X-n; n > 1} be a sequence of i.i.d. mean-zero random variables, and let S-n = Sigma(n)(i) (=1) X-i, n >= 1. We establish necessary and sufficient conditions for having with probability 1, 0 < lim sup(n ->infinity)vertical bar Sn vertical bar/root nh(n) < infinity where h is from a suitable subclass of the positive, nondecreasing slowly varying functions. Specializing our result to h(n) = (log log n)(P), where p > 1 and to h(n) = (log n)(r), r > 0, we obtain analogues of the Hartman-Win...
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作者：Ferrari, PL; Spohn, H
作者单位：Technical University of Munich
摘要：Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(+/- T) = Oconditioned to stay above the semicircle C-T(t) = root T-2 - t(2). In the limit of large T, the fluctuation scale of b(t) - CT(t) is T-1/3 and its time-correlation scale is T-2/3. We prove that, in the sense of weak convergence of path measures, the conditioned Brownian bridge, when properly resealed, converges to a stationary diffusion process with a drift explicitly given in terms of Airy functions...
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作者：Dereich, S; Lifshits, MA
作者单位：Technical University of Berlin; Saint Petersburg State University
摘要：We investigate the Gaussian small ball probabilities with random centers, find their deterministic a.s.-equivalents and establish a relation to infinite-dimensional high-resolution quantization.
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作者：Ferrari, PA; Pimentel, LPR
作者单位：Universidade de Sao Paulo
摘要：The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z(2). We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an asymptot...
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作者：Arnaudon, M; Li, XM
作者单位：Universite de Poitiers; Nottingham Trent University
摘要：We investigate the evolution of barycenters of masses transported by stochastic flows. The state spaces under consideration are smooth affine manifolds with certain convexity structure. Under suitable conditions on the flow and on the initial measure, the barycenter {Z} is shown to be a semimartingale and is described by a stochastic differential equation. For the hyperbolic space the barycenter of two independent Brownian particles is a martingale and its conditional law converges to that of ...
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作者：Khoshnevisan, D; Levin, DA; Méndez-Hernández, PJ
作者单位：Utah System of Higher Education; University of Utah
摘要：Motivated by the recent work of Benjamini, Haggstrom, Peres and Steif [Ann. Probab. 34 (2003) 1-34] on dynamical random walks, we do the following: (i) Prove that, after a suitable normalization, the dynamical Gaussian walk converges weakly to the Ornstein-Uhlenbeck process in classical Wiener space; (ii) derive sharp tail-asymptotics for the probabilities of large deviations of the said dynamical walk; and (iii) characterize (by way of an integral test) the minimal envelope(s) for the growth-...
