3期

最新文章

• The Brownian net AI翻译
  作者：Sun, Rongfeng; Swart, Jan M.
  作者单位：Technical University of Berlin
  摘要：The (standard) Brownian web is a collection of coalescing one-dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net, and study some of its elementary properties.
• Exit from a basin of attraction for stochastic weakly damped nonlinear Schrodinger equations AI翻译
  作者：Gautier, Eric
  作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; ENSAE Paris
  摘要：We consider weakly damped nonlinear Schrodinger equations perturbed by a noise of small amplitude. The small noise is either complex and of additive type or real and of multiplicative type. It is white in time and colored in space. Zero is an asymptotically stable equilibrium point of the deterministic equations. We study the exit from a neighborhood of zero, invariant under the flow of the deterministic equation, in L-2 or in H-1. Due to noise, large fluctuations from zero occur. Thus, on a s...
• Martingale dimensions for fractals AI翻译
  作者：Hino, Masanori
  作者单位：Kyoto University
  摘要：We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math. Sci. 25 (1989) 659-680].
• Borel theorems for random matrices from the classical compact symmetric spaces AI翻译
  作者：Collins, Benoit; Stolz, Michael
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Ottawa; Ruhr University Bochum
  摘要：We study random vectors of the form (Tr(A((1))V),...,Tr(A((r))V)), where V is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the AM are deterministic parameter matrices. We show that for increasing matrix sizes these random vectors converge to a joint Gaussian limit, and compute its covariances. This generalizes previous work of Diaconis et al. for Haar distributed matrices from the classical compact groups. The proof uses integration formulas, ...
• An effective criterion and a new example for ballistic diffusions in random environment AI翻译
  作者：Goergen, Laurent
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：In the setting of multidimensional diffusions in random environment, we carry on the investigation of condition (T'), introduced by Sznitman [Ann. Probab. 29 (2001) 723-764] and by Schmitz [Ann. Inst. H. Poincare Probab. Statist. 42 (2006) 683-714] respectively in the discrete and continuous setting, and which implies a law of large numbers with nonvanishing limiting velocity (ballistic behavior) as well as a central limit theorem. Specifically, we show that when d >= 2, (V) is equivalent to a...
• Local Gaussian fluctuations in the airy and discrete PNG processes AI翻译
  作者：Hagg, Jonas
  作者单位：Royal Institute of Technology
  摘要：We prove that the Airy process, A(t), locally fluctuates like a Brownian motion. In the same spirit we also show that, in a certain scaling limit, the so-called discrete polynuclear growth process (PNG) behaves like a Brownian motion.
• Local limit theorems for finite and infinite urn models AI翻译
  作者：Hwang, Hsien-Kuei; Janson, Svante
  作者单位：Academia Sinica - Taiwan; Uppsala University
  摘要：Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.
• Hitting probability of a distant point for the voter model started with a single 1 AI翻译
  作者：Merle, Mathieu
  作者单位：University of British Columbia
  摘要：The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In dimensions d = 2 or 3, we obtain the precise asymptotic behavior of this probability. We use the scaling limit of the voter model started from a single 1 at the origin in terms of super-Brownian motion under its excursion measure. This invariance principle was stated by Bramson, Cox and Le Gall, as a consequence of a...
• A geometrical structure for an infinite oriented cluster and its uniqueness AI翻译
  作者：Wu, Xian-Yuan; Zuang, Yu
  作者单位：Capital Normal University; University of Colorado System; University of Colorado at Colorado Springs
  摘要：We consider the supercritical oriented percolation model. Let K be all the percolation points. For each u is an element of K, we write Y-u as its rightmost path. Let G = U-u y(u). In this paper, we show that G is a single tree with only one topological end. We also present a relationship between X and G and construct a bijection between K and Z using the preorder traversal algorithm. Through applications of this fundamental graph property, we show the uniqueness of an infinite oriented cluster...
• Stochastic calculus for symmetric Markov processes AI翻译
  作者：Chen, Z. -Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T. -S.
  作者单位：University of Washington; University of Washington Seattle; University of California System; University of California San Diego; Kumamoto University; University of Manchester
  摘要：Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Ito formula for Dirichlet processes is obtained.