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作者：Dubins, Lester E.; Gilat, David; Meilijson, Isaac
作者单位：University of California System; University of California Berkeley; Tel Aviv University
摘要：It is shown that the ratio between the expected diameter of an L-2-bounded martingale and the standard deviation of its last term cannot exceed root 3. Moreover, I one-parameter family of stopping times on standard Brownian motion is exhibited, for which the root 3 upper bound is attained. These stopping times, one for each cost-rate c, are optimal when the payoff for stopping at time t is the diameter D(t) obtained up to time t minus the hitherto accumulated cost ct. A quantity related to dia...
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作者：Koenig, Wolfgang; Lacoin, Hubert; Moerters, Peter; Sidorova, Nadia
作者单位：Leipzig University; Universite Paris Cite; University of Bath; University of London; University College London
摘要：The parabolic Anderson problem is the Cauchy problem for the heat equation partial derivative(t)u(t, z) = Delta u(t,z) + xi(z)u(t,z) on (0,infinity) x Z(d) with random potential (xi(z): z is an element of Z(d)). We consider independent and identically distributed potentials, such that the distribution function of (z) converges polynomially at infinity. If u is initially localized in the origin, that is, if u(0, z) = 1(0)(z), we show that, as time goes to infinity, the solution is completely lo...
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作者：Bloemker, Dirk; Flandoli, Franco; Romito, Marco
作者单位：University of Augsburg; University of Pisa; University of Florence
摘要：The paper analyzes a model in surface growth where the uniqueness of weak solutions seems to be out of reach. We prove existence of a weak martin-gale solution satisfying energy inequalities and having the Markov property. Furthermore, under nondegeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.
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作者：Peterson, Jonathon; Zeitouni, Ofer
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：We consider it nearest-neighbor, one dimensional random walk (X-n)(n >= 0) in a random i.i.d. environment. in the regime where the walk is transient but with zero speed, so that X-n is of order n(s) for some s < 1. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible: There exist sequences {n(k)} and {x(k)} depending on the environment only, such that Xn(k) - x(k) = 0(logn(k))(2) (a localized regime). On the other hand, there exist sequences {t...
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作者：Bressaud, Xavier; Fournier, Nicolas
作者单位：Aix-Marseille Universite; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We consider an interacting particle system (eta(t))t >= 0 with values in {0, 1}(Z), in which each vacant site becomes occupied with rate 1, while each connected component of occupied sites become vacant with rate equal to its size. We show that such a process admits a unique invariant distribution, which is exponentially mixing and can be perfectly simulated. We also prove that for any initial condition, the avalanche process tends to equilibrium exponentially fast, as time increases to infini...
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作者：Lowther, George
摘要：In this paper, we took at the properties of limits of a sequence of real valued inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions, then the limit does not have to be a diffusion. However, we show that as long as the drift terms satisfy a Lipschitz condition and the limit is continuous in probability, then it will lie in a class of processes that we refer to as the almost-continuous diffusions. These processes are strong Markov and satisfy an al...
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作者：Capitaine, Mireille; Donati-Martin, Catherine; Feral, Delphine
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux
摘要：In this paper, we investigate the asymptotic spectrum of complex or real Deformed Wigner matrices (M-N)(N) defined by M-N = W-N/root N + A(N) where W-N is all N x N Hermitian (resp., symmetric) Wigner matrix whose entries have a symmetric law satisfying a Poincare inequality. The matrix A(N) is Hermitian (resp., symmetric) and deterministic with all but finitely many eigenvalues equal to zero. We first show that, as soon as the first largest or last smallest eigenvalues of A(N) are sufficientl...
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作者：Krishnapur, Manjunath
作者单位：University of Toronto
摘要：We consider two families of random matrix-valued analytic functions: (1) G(1) - zG(2) and (2) G(0) + zG(1) + Z(2)G(2) + . . . , where G(i) are n x n random matrices with independent standard complex Gaussian entries. The random set of z where these matrix-analytic functions become singular is shown to be determinantal point processes in the sphere and the hyperbolic plane, respectively. The kernels of these determinantal processes are reproducing kernels of certain Hilbert spaces (Bargmann-Foc...
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作者：Boutillier, Cedric
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：In this paper, we study the bead model: beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two Consecutive beads on a wired there must be exactly one bead on each neighboring wire. We construct a one-parameter family of Gibbs measures on the bead configurations that are uniform in a certain sense. When endowed with one of these measures, this model is shown to be a determinantal point process, whose marginal on each wire...
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作者：Lindner, Alexander; Sato, Ken-iti
作者单位：Braunschweig University of Technology
摘要：Properties of the law mu of the integral f(0)(infinity) C(-N1)-dY(1), are studied, where c > 1 and {(N(1), Y(1)). t >= 0} is a bivariate Levy process such that {N(t)} and {Y(t)} are Poisson processes with parameters a and b, respectively. This is the stationary distribution of some generalized Ornstein-Uhlenbeck process. The law mu is parametrized by c, q and r, where p = 1 - q - r, q, and r are the normalized Levy measure of {(N(t), Y(t))} at the points (1, 0), (0, 1) and (1, 1) respectively....
