Probability Theory and Related Fields

最新文章

• Critical percolation exploration path and SLE 6:: a proof of convergence AI翻译
  作者：Camia, Federico; Newman, Charles M.
  作者单位：Vrije Universiteit Amsterdam; New York University
  摘要：It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE6. We provide here a detailed proof, which relies on Smirnov's theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy's formula). The version of convergence to SLE (6) that we prove suffices for the Smirnov-Werner derivation of certain critical percolation crossing exponents and for our an...
• The Heckman-Opdam Markov processes AI翻译
  作者：Schapira, Bruno
  作者单位：Universite de Orleans; Universite Paris Cite; Sorbonne Universite
  摘要：We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in (Iberoamericana 1...
• 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...
• Asymptotic statistical equivalence for scalar ergodic diffusions AI翻译
  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...
• Acknowledgement of priority concerning On the central limit theorem for geometrically ergodic Markov chains'' AI翻译
  作者：Häggström, O
  作者单位：Chalmers University of Technology
• 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...
• Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks AI翻译
  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...
• Translation invariant Gibbs states for the Ising model AI翻译
  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.
• 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 ...
• Discrete and continuous Yang-Mills measure for non-trivial bundles over compact surfaces AI翻译
  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...