-
作者：Erschler, Anna
作者单位：Universite de Lille
摘要：We prove an isoperimetric inequality for wreath products of Markov chains with variable fibers. We use isoperimetric inequalities for wreath products to estimate the return probability of random walks on infinite groups and graphs, drift of random loops, the expected value E(exp(-tR(n) )), where R (n) is the number of distinct sites, visited up to the moment n, and, more generally, E[exp (-Sigma(z:Lz),(n not equal 0) F(L-z,L-n, z)) (where L-z,L-n is the number of visits of z up to the moment n...
-
作者：Talagrand, Michel
作者单位：Universite Paris Cite; Sorbonne Universite; University System of Ohio; Ohio State University
摘要：Consider the random subset Chi of Nu obtained by selecting independently each integer with a probability delta. Consider a finite class F of finite sets. We describe a combinatorial quantity that is of the same order as E sup(F epsilon F) card (Chi boolean AND F). We then give a related result allowing to compute the supremum of the empirical process on a class of sets.
-
作者：Balogh, J; Bollobás, B
作者单位：University System of Ohio; Ohio State University; University of Memphis; University of Cambridge
摘要：In the bootstrap percolation on the n-dimensional hypercube, in the initial position each of the 2(n) sites is occupied with probability p and empty with probability 1 - p, independently of the state of the other sites. Every occupied site remains occupied for ever, while an empty site becomes occupied if at least two of its neighbours are occupied. If at the end of the process every site is occupied, we say that the ( initial) position spans the hypercube. We shall show that there are constan...
-
作者：Fontes, LRG; Mathieu, P
作者单位：Aix-Marseille Universite
摘要：We study models of continuous time, symmetric, Z(d)-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We consider the case of independent conductances with a polynomial tail near 0 and obtain precise asymptotics for the annealed return probability and convergence times for the random walk confined to a finite box.
-
作者：Gnedin, Alexander; Pitman, Jim; Yor, Marc
作者单位：Utrecht University; University of California System; University of California Berkeley; Sorbonne Universite
摘要：For (R) over tilde = 1-exp(-R) a random closed set obtained by exponential transformation of the closed range R of a subordinator, a regenerative composition of generic positive integer n is defined by recording the sizes of clusters of n uniform random points as they are separated by the points of (R) over tilde. We focus on the number of parts K-n of the composition when (R) over tilde is derived from a gamma subordinator. We prove logarithmic asymptotics of the moments and central limit the...
-
作者：Zhou, Wang; Jing, Bing-Yi
作者单位：National University of Singapore; Hong Kong University of Science & Technology
摘要：In this paper, we derive saddlepoint approximations for Student's t-statistics for strongly nonlattice random variables without moment conditions. Under very mild conditions, we show that saddlepoint equations always have solutions.
-
作者：Klemela, J
作者单位：University of Mannheim
摘要：Estimation of a quadratic functional of a function observed in the Gaussian white noise model is considered. A data-dependent method for choosing the amount of smoothing is given. The method is based on comparing certain quadratic estimators with each other. It is shown that the method is asymptotically sharp or nearly sharp adaptive simultaneously for the regular and irregular region. We consider l(p) bodies and construct bounds for the risk of the estimator which show that for p=4 the estima...
-
作者：Guan, QY; Ma, ZM
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this paper we investigate the reflected symmetric alpha-stable processes and their generators. We show that the generators are regional fractional Laplacians on the closed region. In the case of 1 <= alpha < 2 their existence requires that partial derivative u/partial derivative n = 0 on the boundary. Among other things we obtain the integration by parts formula of the regional fractional Laplacian and the semi-martingale decomposition of the reflected symmetric alpha-stable processes.
-
作者：Umanitá, V
作者单位：University of Genoa
摘要：We show that a QMS on a sigma-finite von Neumann algebra A can be decomposed as the sum of several sub-semigroups corresponding to transient and recurrent projections. We discuss two applications to physical models.
-
作者：Miyokawa, Tomohiro; Shigekawa, Ichiro
作者单位：Kyoto University
摘要：In this paper, we study Schrodinger type operator on a Riemannian manifold. Under some assumptions on a potential function, we characterize the domain of the square root of the Schrodinger type operator on L-p space. In the proof, the defective intertwining properties and the Littlewood-Paley inequalities play important roles.
