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作者：Baik, J; Ben Arous, G; Péché, S
作者单位：University of Michigan System; University of Michigan; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables in each sample become large. When all but finitely many, say r, eigenvalues of the covariance matrix are the same, the dependence of the limiting distribution of the largest eigenvalue of the sample covariance matrix on those distinguished r eigenvalues of the covariance matrix is completely characterized in terms of an infin...
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作者：Penrose, MD
作者单位：University of Bath
摘要：Suppose X = (X-x, x in Z(d)) is a family of i.i.d. variables in some measurable space, B-0 is a bounded set in R-d, and for t > 1, H-t is a measure on t B-0 determined by the restriction of X to lattice sites in or adjacent to t B-0. We prove convergence to a white noise process for the random measure on B0 given by t(-d/2)(H-t(tA) - EHt (tA)) for subsets A of B-0, as t becomes large, subject to H satisfying a stabilization condition (whereby the effect of changing X at a single site x is loca...
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作者：Siegmund, D; Yakir, B
作者单位：Stanford University; Hebrew University of Jerusalem
摘要：An urn model of Diaconis and some generalizations are discussed. A convergence theorem is proved that implies for Diaconis' model that the empirical distribution of balls in the urn converges with probability one to the uniform distribution.
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作者：Konstantinides, DG; Mikosch, T
作者单位：University of Aegean; University of Copenhagen
摘要：In this paper we consider the stochastic recurrence equation Y-t = A(t)Y(t-1) + B-t for an i.i.d. sequence of pairs (A(t), B-t) of nonnegative random variables, where we assume that Bt is regularly varying with index kappa > 0 and EA(t)(kappa) < 1. We show that the stationary solution (Y-t) to this equation has regularly varying finite-dimensional distributions with index K. This implies that the partial sums S-n = Y-1 + - - - + Y-n of this process are regularly varying. In particular, the rel...
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作者：Borgs, C; Chayes, JT; Van der Hofstad, R; Slade, G; Spencer, J
作者单位：Microsoft; University of British Columbia; Eindhoven University of Technology; New York University
摘要：In a previous paper we defined a version of the percolation triangle condition that is suitable for the analysis of bond percolation on a finite connected transitive graph, and showed that this triangle condition implies that the percolation phase transition has many features in common with the phase transition on the complete graph. In this paper we use a new and simplified approach to the lace expansion to prove quite generally that, for finite graphs that are tori, the triangle condition fo...
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作者：Nikeghbali, A; Yor, M
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Recently, Williams [Bull. London Math. Soc. 34 (2002) 610-612]gave an explicit example of a random time rho associated with Brownian motion such that p is not a stopping time but EM rho = EM0 for every bounded martingale M. The aim of this paper is to characterize such random times, which we call pseudo-stopping times, and to construct further examples, using techniques of progressive enlargements of filtrations.
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作者：Heveling, M; Last, G
作者单位：Helmholtz Association; Karlsruhe Institute of Technology
摘要：The paper considers a stationary point process N in Rd. A point-map picks a point of N in a measurable way. It is called bijective [Thorisson, H. (2000). Coupling, Stationarity, and Regeneration. Springer, New York] if it is generating (by suitable shifts) a bijective mapping on N. Mecke [Math. Nachr 65 (1975) 335-344] proved that the Palm measure of N is pointstationary in the sense that it is invariant under bijective point-shifts. Our main result identifies this property as being characteri...
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作者：Samorodnitsky, G
作者单位：Cornell University
摘要：This paper elucidates the connection between stationary symmetric alpha-stable processes with 0 < alpha < 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.
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作者：Bessaih, H; Gubinelli, M; Russo, F
作者单位：University of Wyoming; Universite Paris 13
摘要：We study an evolution problem in the space of continuous loops in a three-dimensional Euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Holder regular loops with index greater than 1/3. When the Holder regularity of the initial condition X is smaller or equal to 1/2, we require X to be a rough path in the sense of Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310, System Control and Rough...
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作者：Cheliotis, D
作者单位：University of Toronto
摘要：According to a theorem of Schumacher and Brox, 2 for a diffusion X in a Brownian environment, it holds that (X-t - b(log)t)/log(2) t -> 0 in probability, as t -> infinity, where b is a stochastic process having an explicit description and depending only on the environment. We compute the distribution of the number of sign changes for b on an interval [1, x] and study some of the consequences of the computation; in particular, we get the probability of b keeping the same sign on that interval. ...
