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作者：Sly, Allan; Zhang, Yumeng
作者单位：Australian National University; University of California System; University of California Berkeley
摘要：The mixing time of the Glauber dynamics for spin systems on trees is closely related to the reconstruction problem. Martinelli, Sinclair and Weitz established this correspondence for a class of spin systems with soft constraints bounding the log-Sobolev constant by a comparison with the block dynamics [ Comm. Math. Phys. 250 (2004) 301-334; Random Structures Algorithms 31 (2007) 134-172]. However, when there are hard constraints, the dynamics inside blocks may be reducible. We introduce a vari...
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作者：Henry-Labordere, Pierre; Tan, Xiaolu; Touzi, Nizar
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：We propose an unbiased Monte 3 estimator for E [g(X-t1,..., X-tn)], where X is a diffusion process defined by a multidimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen simulatable SDE whose coefficients are updated at independent exponential times. Such a simulatable process can be viewed as a regime-switching SDE, or as a branching diffusion process with one single living particle at all times. In order to compensate for the change of the ...
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作者：Doering, Leif; Klenke, Achim; Mytnik, Leonid
作者单位：University of Mannheim; Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：For many stochastic diffusion processes with mean field interaction, convergence of the rescaled total mass processes towards a diffusion process is known. Here, we show convergence of the so-called finite system scheme for interacting jump-type processes known as mutually catalytic branching processes with infinite branching rate. Due to the lack of second moments, the rescaling of time is different from the finite rate mutually catalytic case. The limit of rescaled total mass processes is id...
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作者：Hambly, Ben; Ledger, Sean
作者单位：University of Oxford; University of Bristol
摘要：We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes large, the empirical measure of the population converges to the solution of a nonlinear stochastic heat equation with Dirichlet boundary condition. The diffusion coefficients are allowed to have finitely many discontinuities (piecewise Lipschitz) and we prov...
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作者：Chetrite, Raphael; Diel, Roland; Lerasle, Matthieu
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Ton Duc Thang University; Ton Duc Thang University
摘要：We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely, the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number of potential winners. First, we prove that under moment and convexity conditions, the asymptotic probability that the best player wins is 1. The convexity condition is natural when the distribution of strengths is unbounded and, in the bounded case, when t...
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作者：Durmus, Alain; Moulines, Eric
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：In this paper, we study a method to sample from a target distribution pi over R-d having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with pi. For both constant and decreasing step sizes in the Euler discretization, we obtain nonasymptotic bounds for the convergence to the target distribution pi in total variation distance. A pa...
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作者：Kolodziejek, Bartosz
作者单位：Warsaw University of Technology
摘要：In this paper, we show under weak assumptions that for R = (d) 1 + M-1 M1M2 + . . ., where P(M is an element of [0, 1]) = 1 and M-i are independent copies of M, we have lnP(R > x) similar to CxlnP(M > 1 - 1/x) as x -> infinity. The constant C is given explicitly and its value depends on the rate of convergence of 1nP(M > 1 - 1/x). Random variable R satisfies the stochastic equation R 1 + MR with M and R independent, thus this result fits into the study of tails of iterated random equations, or...
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作者：Braverman, Anton; Dai, J. G.
作者单位：Cornell University
摘要：We consider M/Ph/n + M queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein Uhlenbeck (OU) process is bounded by C/root T., where the constant C is independent of the arrival rate A and the number of servers n as long as they are in the HalfinWhitt parameter regime. For each integer m > 0, we also establish a similar bound for the difference of the mth steady-state mom...
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作者：Chen, Guan-Yu; Hsu, Jui-Ming; Sheu, Yuan-Chung
作者单位：National Yang Ming Chiao Tung University
摘要：In this article, we considers reversible Markov chains of which L-2-distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discussed by Chen and Saloff-Coste in [J. Funct. Anal. 258 (2010) 2246-2315], while we provide here a completely different pathway to analyze the L-2-distance. Consequently, we obtain several considerably simplified criteria and this allows us to proceed advanced theoretical studies, including the comparison of cutoffs between...
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作者：Jarai, Antal A.
作者单位：University of Bath
摘要：We study the following game on a finite graph G = (V,E). Each edge e is an element of E starts with an integer value n(e) >= 0, and we write n = Sigma eE n(e). At time t, 1 <= t <= n, a uniformly random vertex v is an element of V is generated, and one of the edges f incident with v must be selected. The value of f is then decreased by 1. There is a unit final reward if the configuration (0,...,0) is reached. Our main result is that there is a phase transition: as n -> infinity, the expected r...
