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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-...
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作者：Gadidov, A
作者单位：University System of Georgia; Kennesaw State University
摘要：In this note we show that almost sure convergence to zero of symmetrized U-statistics indexed by a linear sector in Z(+)(d) is equivalent to convergence along the diagonal of Z(+)(d), as it is considered in Latala and Zinn [Ann. Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums of multiindexed i.i.d. random variables are also made.
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作者：Bass, RF; Rosen, J
作者单位：University of Connecticut; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：For a symmetric random walk in Z(2) with 2 + delta moments, we represent vertical bar R(n)vertical bar, the cardinality of the range, in terms of an expansion involving the renormalized intersection local times of a Brownian motion. We show that for each k >= 1 [Graphics] where Wt is a Brownian motion, W(t)((n)) = Wnt/root n, gamma j,n is the renormalized intersection local time at time 1 for W((n)) and c(X) is a constant depending on the distribution of the random walk.
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作者：Benaïm, M; Raimond, O
作者单位：University of Neuchatel; Universite Paris Saclay
摘要：Let M be a compact Riemannian manifold. A self-interacting diffusion on M is a stochastic process solution to where {W-t} is a Brownian vector field on M and V-x(y) = V(x, y) a smooth function. Let mu(t) = 1/t integral(t)(0) delta X-s ds denote the normalized occupation measure of X-t. We prove that, when V is symmetric, mu(t) converges almost surely to the critical set of a certain nonlinear free energy functional J. Furthermore, J has generically finitely many critical points and mu(t) conve...
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作者：Ignatiouk-Robert, I
作者单位：CY Cergy Paris Universite
摘要：This paper is devoted to the problem of sample path large deviations for the Markov processes on RN having a constant but different transition mechanism oil each boundary set {x: x(i) = 0 for i is not an element of Lambda, x(i) > 0 for i is an element of Lambda). The global sample path large deviation principle and an integral representation of the rate function are derived from local large deviation estimates. Our results complete the proof of Dupuis and Ellis of the sample path large deviati...
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作者：van der Vaart, A; van Zanten, H
作者单位：Vrije Universiteit Amsterdam
摘要：We consider the empirical process G(t) of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions, the finite-dimensional distributions of G(t) converge weakly to those of a zero-mean Gaussian random process G. We prove that the weak convergence G(t) double right arrow G takes place in l(infinity)(F) if and only if the limit G exists as a tight, Borel measurable map. The proof relies on majorizing measure techni...
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作者：Benaych-Georges, F
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We construct a random matrix model for the bijection Psi between classical and free infinitely divisible distributions: for every d >= 1, we associate in a quite natural way to each *-infinitely divisible distribution P a distribution P-d(mu) on the space of d x d Hermitian matrices such that P-d(mu) * P-d(v) = P-d(mu*v). The spectral distribution of a random matrix with distribution P-d(mu) converges in d probability to Psi(mu) when d tends to +infinity. It gives, among other things, a new pr...
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作者：Johansson, K
作者单位：Royal Institute of Technology
摘要：We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure of the tiling at the center of the Aztec diamond.
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作者：Goldschmidt, C
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical, The phase transition takes various forms, depending on the values of the parameters controlling the different types of hyperedges. It may be continuous as in a random graph. (In fact, when there are no higher-order edges, it is exactly the emergence of the giant component.) ...
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作者：Hu, YZ; Nualart, D
作者单位：University of Kansas; University of Barcelona
摘要：Let B-t(H) H be a d-dimensional fractional Brownian motion with Hurst parameter H E (0, 1). Assume d ≥ 2. We prove that the renormalized self-intersection local time L = ∫(T)(0) ∫(t)(0) δ(B-t(H) - B-s(H)) ds dt - E(∫(T)(0) ∫(t)(0) δ(B-t(H) -B-s(H)) ds dt) exists in L-2 if and only if H < 3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a result of Yor, we show that in the case 3/4 > H ≥ 3/2d, r(ε)Lε converges i...
