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作者：Gine, Evarist; Koltchinskii, Vladimir
作者单位：University of Connecticut; University of New Mexico
摘要：Let F be a class of measurable functions on a measurable space (S, S) with values in [0, 1] and let [GRAPHICS] be the empirical measure based on an i.i.d. sample (X-1,..., X-n) from a probability distribution P on (S, S). We study the behavior of suprema of the following type: [GRAPHICS] where sigma(p)f >= Var(p)(1/2) f and phi is a continuous, strictly increasing function with phi(0) = 0. Using Talagrand's concentration inequality for empirical processes, we establish concentration inequaliti...
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作者：Sheffield, Scott
作者单位：University of California System; University of California Berkeley
摘要：An essential spanning forest of an infinite graph G is a spanning forest of G in which all trees have infinitely many vertices. Let G(n) be an increasing sequence of finite connected subgraphs of G for which boolean OR G(n) = G. Pemantle's arguments imply that the uniform measures on spanning trees of G, converge weakly to an Aut(G)-invariantmeasure mu(G) on essential spanning forests of G. We show that if G is a connected, amenable graph and F subset of Aut(G) acts quasitransitively on G, the...
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作者：Evans, Steven N.; Winter, Anita
作者单位：University of California System; University of California Berkeley; University of Erlangen Nuremberg
摘要：We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis. A key technical ingredient in this work is the use of a novel Gromov-Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Di...
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作者：Chassaing, Philippe; Durhuus, Bergfinnur
作者单位：Universite de Lorraine; University of Copenhagen; University of Copenhagen
摘要：Exploiting a bijective correspondence between planar quadrangulations and well-labeled trees, we define an ensemble of infinite surfaces as a limit of uniformly distributed ensembles of quadrangulations of fixed finite volume. The limit random surface can be described in terms of a birth and death process and a sequence of multitype Galton-Watson trees. As a consequence, we find that the expected volume of the ball of radius r around a marked point in the limit random surface is Theta(r(4)).
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作者：Mathieu, Pierre
作者单位：Aix-Marseille Universite
摘要：We extend the Carne-Varopoulos upper bound on the probability transitions of a Markov chain to a certain class of nonreversible processes by introducing the definition of a centering measure. In the case of random walks on a group, we study the connections between different notions of centering.
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作者：Timar, Adam
作者单位：Indiana University System; Indiana University Bloomington
摘要：We show that for a transitive unimodular graph, the number of ends is the same for every tree of the free minimal spanning forest. This answers a question of Lyons, Peres and Schramm.
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作者：Chen, Zhen-Qing; Fukushima, Masatoshi; Ying, Jiangang
作者单位：University of Washington; University of Washington Seattle; Kansai University; Fudan University
摘要：Time change is one of the most basic and very useful transformations for Markov processes. The time changed process can also be regarded as the trace of the original process on the support of the Revuz measure used in the time change. In this paper we give a complete characterization of time changed processes of an arbitrary symmetric Markov process, in terms of the Beurling-Deny decomposition of their associated Dirichlet forms and of Feller measures of the process. In particular, we determin...
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作者：Caballero, M. E.; Chaumont, L.
作者单位：Universidad Nacional Autonoma de Mexico; Universite Paris Cite; Sorbonne Universite
摘要：Using Lamperti's relationship between Levy processes and positive selfsimilar Markov processes (pssMp), we study the weak convergence of the law P., of a pssMp starting at x > 0, in the Skorchod space of cadlag paths, when x tends to 0. To do so, we first give conditions which allow us to construct a cadlag Markov process X-(0), starting from 0, which stays positive and verifies the scaling property. Then we establish necessary and sufficient conditions for the laws P-x to converge weakly to t...
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作者：Nourdin, Ivan; Simon, Thomas
作者单位：Universite de Lorraine; Universite Paris Saclay
摘要：We consider the problem of absolute continuity for the one-dimensional SDE [GRAPHICS] where Z is a real Levy process without Brownian part and a a function of class C-1 with bounded derivative. Using an elementary stratification method, we show that if the drift a is monotonous at the initial point x, then X-t is absolutely continuous for every t > 0 if and only if Z jumps infinitely often. This means that the drift term has a regularizing effect, since Z(t) itself may not have a density. We a...
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作者：Daviaud, Olivier
作者单位：Stanford University
摘要：We consider the lattice version of the free field in two dimensions and study the fractal structure of the sets where the field is unusually high (or low). We then extend some of our computations to the case of the free field conditioned on being everywhere nonnegative. For example, we compute the width of the largest downward spike of a given length. Through the prism of these results, we find that the extrema of the free field under entropic repulsion (minus its mean) and those of the uncond...
