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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...
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作者：Dalalyan, A; Reiss, M
作者单位：Sorbonne Universite; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：For scalar diffusion models with unknown drift function asymptotic equivalence in the sense of Le Cam's deficiency between statistical experiments is considered under long-time asymptotics. A local asymptotic equivalence result is established with an accompanying sequence of simple Gaussian shift experiments. Corresponding globally asymptotically equivalent experiments are obtained as compound experiments. The results are extended in several directions including time discretisation. An explici...
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作者：Häggström, O
作者单位：Chalmers University of Technology
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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...
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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...
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作者：Bodineau, T
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases mu(+)(beta), mu(-)(beta) for any beta not equal beta(c). This implies that the average magnetization is continuous for beta > beta(c). Furthermore, combined with previous results on the slab percolation threshold [B2] this shows the validity of Pisztora's coarse graining [ Pi] up to the critical temperature.
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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 ...
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作者：Levy, Thierry
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this paper, we construct one Yang-Mills measure on an orientable compact surface for each isomorphism class of principal bundles with compact connected structure group over this surface. For this, we refine the discretization procedure used in a previous construction [9] and define a discrete theory on a new configuration space which is essentially a covering of the usual one. We prove that the measures corresponding to different isomorphism classes of bundles or to different total areas of...
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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.
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作者：Hammond, PJ; Sun, YN
作者单位：Stanford University; National University of Singapore; National University of Singapore
摘要：For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown to be essentially equivalent - i.e., equivalent to up to null sets. Unlike in the finite setting, a large collection of random variables remains essentially conditionally independent under further conditioning. The essential equivalence of pairwise and multiple versions of exchangeability also follows as a corollary. Our result relies on an iterated extension of Bledsoe a...
