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• Gaussian estimates for spatially inhomogeneous random walks on Zd AI翻译
  作者：Mustapha, S
  作者单位：Universite Paris Cite; Sorbonne Universite
  摘要：It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on Z(d) admits upper and lower Gaussian estimates.
• Spectral measure of large random Hankel, Markov and Toeplitz matrices AI翻译
  作者：Bryc, W; Dembo, A; Jiang, TF
  作者单位：University System of Ohio; University of Cincinnati; Stanford University; Stanford University; University of Minnesota System; University of Minnesota Twin Cities
  摘要：We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables {X-k} of unit variance, and for symmetric Markov matrices generated by i.i.d. random variables {X-ij} (j > i) of zero mean and unit variance, scaling the eigen-values by root n we prove the almost sure, weak convergence of the spectral measures to universal, nonrandom, symmetric distributions gamma(H), gamma(M) and gamma(...
• Random growth models with polygonal shapes AI翻译
  作者：Gravner, J; Griffeath, D
  作者单位：University of California System; University of California Davis; University of Wisconsin System; University of Wisconsin Madison
  摘要：We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and then establish the validity of the Wulff construction for asymptotic shapes arising from finite initial seeds. Such a shape converges to the polygonal invariant shape of the corresponding deterministic model as the perturbation decreases. In many cases, exact stability is observed. That is, for small perturbations, t...
• On random almost periodic trigonometric polynomials and applications to ergodic theory AI翻译
  作者：Cohen, G; Cuny, C
  作者单位：Ben-Gurion University of the Negev
  摘要：We study random exponential sums of the form Sigma(n)(k=1) X-k exp {i (lambda((1))(k) t(1) +(...)+ lambda((s))(k)t(s))}, where {X-n} is a sequence of random variables and {lambda((i))(n) : 1 <= i <= s} are sequences of real numbers. We obtain uniform estimates (on compact sets) of such sums, for independent centered {X-n} or bounded {X-n} satisfying some mixing conditions. These results generalize recent results of Weber [Math. Inequal. Appl. 3 (2000) 443-457] and Fan and Schneider [Ann. Inst....
• Late points for random walks in two dimensions AI翻译
  作者：Dembo, A; Peres, Y; Rosen, J; Zeitouni, O
  作者单位：Stanford University; Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; University of California System; University of California Berkeley; Technion Israel Institute of Technology; Technion Israel Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
  摘要：Let T-n(x) denote the time of first visit of a point x on the lattice torus Z(n)(2) = Z(2)/nZ(2) by the simple random walk. The size of the set of alpha, n-late points L-n(alpha) = {x is an element of Z(n)(2): T-n(x) >= alpha(4)/(pi)(n log n)(2)} is approximately n(2(1-alpha)), for alpha is an element of (0, 1) [L-n(alpha) is empty if alpha > 1 and n is large enough]. These sets have interesting clustering and fractal properties: we show that for beta is an element of (0, 1), a disc of radius ...
• Improper regular conditional distributions (vol 34, pg 423, 2006) AI翻译
  作者：Seidenfeld, T; Schervish, MJ; Kadane, JB
  作者单位：Carnegie Mellon University; Carnegie Mellon University
• Central limit theorems for additive functionals of the simple exclusion process (vol 34, pg 427, 2006) AI翻译
  作者：Sethuraman, S
  作者单位：Iowa State University
• Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices AI翻译
  作者：Chan, HP; Lai, TL
  作者单位：National University of Singapore; Stanford University
  摘要：Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in change-point and signal detection as special cases. Some key ingredients in these extensions are moderate deviation approximations to marginal tail probabilities and weak convergence of the conditional distributi...
• A Gaussian kinematic formula AI翻译
  作者：Taylor, JE
  作者单位：Stanford University
  摘要：In this paper we consider probabilistic analogues of some classical integral geometric formulae: Weyl-Steiner tube formulae and the Chern-Federer kinematic fundamental formula. The probabilistic building blocks are smooth, real-valued random fields built up from i.i.d. copies of centered, unit-variance smooth Gaussian fields on a manifold M. Specifically, we consider random fields of the form f(p) = F(y(1) (p),..., y(k) (p)) for F is an element of C-2 (R-k ; R) and (y(1),..., y(k)) a vector of...
• Notes on the two-dimensional, fractional Brownian motion AI翻译
  作者：Baudoin, F; Nualart, D
  作者单位：University of Barcelona
  摘要：We study the two-dimensional fractional Brownian motion with Hurst parameter H > (1)/(2). In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.