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最新文章

• Strengthening classical results on convergence rates in strong limit theorems AI翻译
  作者：Spataru, Aurel
  作者单位：Romanian Academy; Institute of Mathematical Statistics & Applied Mathematics of Romanian Academy
  摘要：Let X-1, X-2, . . . be i.i.d. random variables, and set S-n=X-1+ . . . +X-n. Several authors proved convergence of series of the type f(epsilon)=Sigma(n)c(n)P(|S-n| > epsilon a(n)), epsilon >alpha, under necessary and sufficient conditions. We show that under the same conditions, in fact integral(infinity)(delta) f(epsilon)d epsilon < infinity, delta > alpha, i.e. the finiteness of Sigma(n)c(n)P(|S-n| > epsilon a(n)), epsilon >alpha, is equivalent to the convergence of the double sum Sigma(k)S...
• Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree AI翻译
  作者：Caputo, Pietro; Martinelli, Fabio
  作者单位：Sapienza University Rome
  摘要：Consider a low temperature stochastic Ising model in the phase coexistence regime with Markov semigroup P-t. A fundamental and still largely open problem is the understanding of the long time behavior of delta P-eta(t) when the initial configuration eta is sampled from a highly disordered state nu (e.g. a product Bernoulli measure or a high temperature Gibbs measure). Exploiting recent progresses in the analysis of the mixing time of Monte Carlo Markov chains for discrete spin models on a regu...
• Markov processes on partitions AI翻译
  作者：Borodin, A; Olshanski, G
  作者单位：California Institute of Technology; Kharkevich Institute for Information Transmission Problems of the RAS
  摘要：We introduce and study a family of Markov processes on partitions. The processes preserve the so-called z-measures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group. We show that the dynamical correlation functions of these processes have determinantal structure and we explicitly compute their correlation kernels. We also compute the scaling limits of the kernels in two different regimes. The limit kernels describe the asymptotic behavior of ...
• Limit theorems for reinforced random walks on certain trees AI翻译
  作者：Collevecchio, Andrea
  作者单位：G d'Annunzio University of Chieti-Pescara
  摘要：Consider a linearly edge-reinforced random walk defined on the b-ary tree, b >= 70. We prove the strong law of large numbers for the distance of this process from the root. We give a sufficient condition for this strong law to hold for general edge-reinforced random walks and random walks in a random environment. We also provide a central limit theorem.
• On the spectrum of Markov semigroups via sample path large deviations AI翻译
  作者：Ignatiouk-Robert, I
  作者单位：CY Cergy Paris Universite
  摘要：The essential spectral radius of a sub-Markovian process is defined as the infimum of the spectral radiuses of all local perturbations of the process. When the family of rescaled processes satisfies sample path large deviation principle, the spectral radius and the essential spectral radius are expressed in terms of the rate function. The paper is motivated by applications to reflected diffusions and jump Markov processes describing stochastic networks for which the sample path large deviation...