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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.
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作者：Bérard, J
作者单位：Universite Claude Bernard Lyon 1
摘要：We study the asymptotic behavior of two mutation-selection genetic algorithms in random environments. First, the state space is a supercritical Galton-Watson tree conditioned upon non-extinction and the objective function is the distance from the root. In the second case, the state space is a regular tree and the objective function is a sample of a tree-indexed random walk. We prove that, after n steps, the algorithms find the maximum possible value of the objective function up to a finite ran...
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作者：van den Berg, M; Bolthausen, E; den Hollander, F
作者单位：University of Bristol; University of Zurich
摘要：In this paper we consider a standard Brownian motion in R-d, starting at 0 and observed until time t. The Brownian motion takes place in the presence of a Poisson random field of traps, whose centers have intensity nu(t) and whose shapes are drawn randomly and independently according to a probability distribution Pi, on the set of closed subsets of R-d, subject to appropriate conditions. The Brownian motion is killed as soon as it hits one of the traps. With the help of a large deviation techn...
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作者：Franke, B
作者单位：Ruhr University Bochum; National Cheng Kung University
摘要：We prove a functional central limit theorem for diffusions on periodic sub- manifolds of R-N. The proof is an adaptation of a method presented in [BenLioPap] and [Bha] for proving functional central limit theorems for diffusions with periodic drift vectorfields. We then apply the central limit theorem in order to obtain a recurrence and a transience criterion for periodic diffusions. Other fields of applications could be heat-kernel estimates, similar to the ones obtained in [Lot].
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作者：Barndorff-Nielsen, OE; Thorbjornsen, S
作者单位：Aarhus University; University of Southern Denmark
摘要：In this paper we prove the free analog of the Levy-Ito decomposition for Levy processes. A significant part of the proof consists of introducing free Poisson random measures, proving their existence and developing a theory of integration with respect to such measures. The existence of free Poisson random measures also yields, via the free Levy-Ito decomposition, an alternative proof of the general existence of free Levy processes ( in law).
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作者：Häggström, O
作者单位：Chalmers University of Technology
摘要：Let X-0,X-1,... be a geometrically ergodic Markov chain with state space X and stationary distribution pi. It is known that if h:X -> R satisfies pi(vertical bar h vertical bar(2+epsilon)) < infinity for some epsilon > 0, then the normalized sums of the X-i's obey a central limit theorem. Here we show, by means of a counterexample, that the condition pi(vertical bar h vertical bar(2+epsilon)) < infinity cannot be weakened to only assuming a finite second moment, i.e., pi(h(2)) < infinity.
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作者：Kempe, J
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：This paper addresses the question: what processes take polynomial time on a quantum computer that require exponential time classically? We show that the hitting time of the discrete time quantum walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum walks. We provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its st...
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作者：Berger, N; Kenyon, C; Mossel, E; Peres, Y
作者单位：University of California System; University of California Berkeley; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We show that the relaxation time (defined as the reciprocal of the spectral gap \lambda(1) - lambda(2)\) for the dynamics on trees and on planar hyperbolic graphs, is polynomial in n. For these hyperbolic graphs, this yields a general polynomial sampling algorithm for random configurations. We then show...
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作者：Aldous, D; Miermont, G; Pitman, J
作者单位：University of California System; University of California Berkeley; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite numbe...
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作者：Denis, L; Matoussi, A; Stoica, L
作者单位：Universite Paris Saclay; Le Mans Universite; University of Bucharest
摘要：In this paper we prove L-p estimates (p >= 2) for the uniform norm of the paths of solutions of quasilinear stochastic partial differential equations (SPDE) of parabolic type. Our method is based on a version of Moser's iteration scheme developed by Aronson and Serrin in the context of non-linear parabolic PDE.
