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作者：Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We prove that the distance between two reflected Brownian motions, driven by the same white noise, outside a sphere in a 3-dimensional flat torus does not converge to 0, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.
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作者：Ben Arous, Gerard; Bourgade, Paul
作者单位：New York University; Harvard University
摘要：This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth smallest gap, normalized by a factor n(-4/3), has a limiting density proportional to x(3k-1)e(-x3). Concerning the largest gaps, normalized by n/root log n, they converge in L-p to a constant for all p > 0. These results are compared with the extreme gaps betw...
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作者：Sethuraman, Sunder; Varadhan, S. R. S.
作者单位：University of Arizona; New York University
摘要：Laws of large numbers, starting from certain nonequilibrium measures, have been shown for the integrated current across a bond, and a tagged particle in one-dimensional symmetric nearest-neighbor simple exclusion [Ann. Inst. Henri Poincare Probab. Stat. 42 (2006) 567-577]. In this article, we prove corresponding large deviation principles and evaluate the rate functions, showing different growth behaviors near and far from their zeroes which connect with results in [J. Stat. Phys. 136 (2009) 1...
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作者：Berestycki, Julien; Berestycki, Nathanael; Schweinsberg, Jason
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; University of Cambridge; University of California System; University of California San Diego
摘要：We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (log N)(3), in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process...
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作者：Crawford, Nicholas; Sly, Allan
作者单位：Technion Israel Institute of Technology; University of California System; University of California Berkeley
摘要：We study limit laws for simple random walks on supercritical long-range percolation clusters on Z(d), d >= 1. For the long range percolation model, the probability that two vertices x, y are connected behaves asymptotically as parallel to x - y parallel to(-s)(2). When s is an element of (d, d + 1), we prove that the scaling limit of simple random walk on the infinite component converges to an a-stable Levy process with alpha = s - d establishing a conjecture of Berger and Biskup [Probab. Theo...
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作者：Adler, Robert J.; Samorodnitsky, Gennady; Taylor, Jonathan E.
作者单位：Technion Israel Institute of Technology; Cornell University; Stanford University
摘要：We consider smooth, infinitely divisible random fields (X (t), t is an element of M), M subset of R-d, with regularly varying Levy measure, and are interested in the geometric characteristics of the excursion sets A(u) = {t is an element of M : X(t) > u} over high levels u. For a large class of such random fields, we compute the u -> infinity asymptotic joint distribution of the numbers of critical points, of various types, of X in A(u), conditional on A(u) being nonempty. This allows us, for ...
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作者：Fribergh, Alexander
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse
摘要：We study the biased random walk in positive random conductances on Z(d). This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite mean. Moreover, in the sub-ballistic regime we find the polynomial order of the distance moved by the particle. This extends results obtained by Shen [Ann. Appl. Probab. 12 (2002) 477-510], who proved positivity of the speed in the uniformly elliptic setting.
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作者：Hammond, Alan
作者单位：University of Oxford
摘要：We consider a random walk on a supercritical Galton-Watson tree with leaves, where the transition probabilities of the walk are determined by biases that are randomly assigned to the edges of the tree. The biases are chosen independently on distinct edges, each one according to a given law that satisfies a logarithmic nonlattice condition. We determine the condition under which the walk is sub-ballistic, and, in the sub-ballistic regime, we find a formula for the exponent gamma epsilon (0, 1) ...
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作者：Bednorz, Witold
作者单位：University of Warsaw
摘要：In this paper we prove the complete characterization of a.s. convergence of orthogonal series in terms of existence of a majorizing measure. It means that for a given (a(n))(n=1)(infinity), a(n) > 0, series Sigma(infinity)(n=1) a(n)phi(n) is a.e. convergent for each orthonormal sequence (phi(n))(n=1)(infinity) if and only if there exists a measure m on T = {0} boolean OR {Sigma(m)(n=1) a(n)(2), m >= 1} such that sup(t is an element of T)integral(root D(T))(0) (m(B(t, r(2))))(-1/2) dr < infinit...
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作者：Junge, Marius; Zeng, Qiang
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and Pinelis, Utev for commutative random variables. We also present new best constants in Rosenthal's inequality. Applying these results to random Fourier projections, we recover and elaborate on fundamental results from compressed sensing, due to Candes, Romberg and Tao.
