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作者：Basrak, Bojan; Krizmanic, Danijel; Segers, Johan
作者单位：University of Zagreb; University of Rijeka; Universite Catholique Louvain
摘要：Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version of this is known to be true as well, the limit process being a stable Levy process. The main result in the paper is that for a stationary, regularly varying sequence for which clusters of high-threshold excesses can be broken down into asymptotically indepe...
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作者：Cohen, Samuel N.; Elliott, Robert J.
作者单位：University of Oxford; University of Adelaide; University of Calgary
摘要：We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and ...
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作者：Ben Arous, Gerard; Fribergh, Alexander; Gantert, Nina; Hammond, Alan
作者单位：New York University; University of Munster; University of Oxford
摘要：We consider a biased random walk X-n on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant gamma = gamma(beta) is an element of (0, 1), depending on the bias beta, such that vertical bar X-n vertical bar is of order n(gamma). Denoting Delta(n) the hitting time of level n, we prove that Delta(n)/n(1/gamma) is tight. Moreover, we show that Delta(n)/n(1/gamma) does not converge in law (at least for large values of beta). We prove that alo...
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作者：Bhamidi, Shankar; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology
摘要：We find scaling limits for the sizes of the largest components at criticality for rank-1 inhomogeneous random graphs with power-law degrees with power-law exponent tau. We investigate the case where tau is an element of (3,4), so that the degrees have finite variance but infinite third moment. The sizes of the largest clusters, resealed by n(-(tau-2)/(tau-1)), converge to hitting times of a thinned Levy process, a special case of the general multiplicative coalescents studied by Aldous [Ann. P...
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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.
