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作者：Beffara, V.; Duminil-Copin, H.
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Geneva
摘要：In a recent and celebrated article, Smirnov [Ann. of Math. (2) 172 (2010) 1435-1467] defines an observable for the self-dual random-cluster model with cluster weight q = 2 on the square lattice Z(2), and uses it to obtain conformal invariance in the scaling limit. We study this observable away from the self-dual point. From this, we obtain a new derivation of the fact that the self-dual and critical points coincide, which implies that the critical inverse temperature of the Ising model equals ...
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作者：Tarres, Pierre; Toth, Balint; Valko, Benedek
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Budapest University of Technology & Economics; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the asymptotic behavior of a self-interacting one-dimensional Brownian polymer first introduced by Durrett and Rogers [Probab. Theory Related Fields 92 (1992) 337-349] The polymer describes a stochastic process with a drift which is a certain average of its local time. We show that a smeared out version of the local time function as viewed from the actual position of the process is a Markov process in a suitably chosen function space, and that this process has a Gaussian stationary me...
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作者：Diaconis, Persi; Ram, Arun
作者单位：Stanford University; Stanford University; University of Melbourne
摘要：The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in the power sum polynomials. The Markov chain has stationary distribution a new two-parameter family of measures on partitions, the inverse of the Macdonald weight (rescaled). The uniform distribution on cycles of permutations and the Ewens sampling formula ar...
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作者：Williams, John D.
作者单位：Indiana University System; Indiana University Bloomington
摘要：Let mu be a probability measure on the real line. In this paper we prove that there exists a decomposition mu = mu(0) boxed plus mu(1) boxed plus ... boxed plus mu(n) boxed plus ... such that mu(0) is infinitely divisible, and mu(i) is indecomposable for i >= 1. Additionally, we prove that the family of all boxed plus-divisors of a measure mu is compact up to translation. Analogous results are also proven in the case of multiplicative convolution.
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作者：Abraham, Romain; Delmas, Jean-Francois
作者单位：Universite de Orleans; Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：We present a construction of a Levy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov theorem. We also extend the pruning procedure to this super-critical case. Let psi be a critical branching mechanism. We set psi(theta)(.) = psi(. + theta) - psi(theta). Let Theta = (theta(infinity), +infinity) or Theta = [theta(infinity), +infinity) be the set of values of theta for which psi(theta) is a cons...
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作者：Benjamini, Itai; Boucheron, Stephane; Lugosi, Gabor; Rossignol, Raphael
作者单位：Weizmann Institute of Science; Pompeu Fabra University; ICREA; Pompeu Fabra University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c is an element of ]0, 1[, the property that the random sub-graph contains a giant component of size c vertical bar V vertical bar has a sharp threshold.
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作者：Chen, Zhen-Qing; Kim, Panki; Song, Renming
作者单位：University of Washington; University of Washington Seattle; Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
摘要：Suppose that d >= 2 and alpha is an element of (1, 2). Let D be a bounded C-1,C-1 open set in R-d and b an R-d-valued function on R-d whose components are in a certain Kato class of the rotationally symmetric a-stable process. In this paper, we derive sharp two-sided heat kernel estimates for L-b = Delta(alpha/2) + b . del in D with zero exterior condition. We also obtain the boundary Harnack principle for L-b in D with explicit decay rate.
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider continuous time random interlacements on Z(d), d >= 3, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the two-dimensional Gaussian free field pinned at the origin by looking at scaled differences of occupation times of long rods by random interlacements at appropriately tuned levels. In the main asymptotic regime, a scaling factor appears in the limit, which is independent of the free fi...
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作者：Drewitz, Alexander; Ramirez, Alejandro F.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Pontificia Universidad Catolica de Chile
摘要：Consider a random walk in an uniformly elliptic environment in dimensions larger than one. In 2002, Sznitman introduced for each gamma is an element of (0, 1) the ballisticity condition (T)(gamma) and the condition (T') defined as the fulfillment of (T)gamma for each gamma is an element of (0, 1). Sznitman proved that (T') implies a ballistic law of large numbers. Furthermore, he showed that for all gamma is an element of (0.5, 1), (T)gamma is equivalent to (T'). Recently, Berger has proved th...
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作者：McGoff, Kevin
作者单位：University System of Maryland; University of Maryland College Park
摘要：Let X be an irreducible shift of finite type (SFT) of positive entropy, and let B-n(X) be its set of words of length n. Define a random subset omega of B-n(X) by independently choosing each word from B-n(X) with some probability alpha. Let X-omega be the (random) SET built from the set omega. For each 0 <= alpha <= 1 and n tending to infinity, we compute the limit of the likelihood that X-omega is empty, as well as the limiting distribution of entropy for X-omega. For alpha near 1 and n tendin...
