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作者：Curien, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：Pursuing the approach of Angel and Ray (Ann Probab, 2015) we introduce and study a family of random infinite triangulations of the full-plane that satisfy a natural spatial Markov property. These new random lattices naturally generalize Angel and Schramm's uniform infinite planar triangulation (UIPT) and are hyperbolic in flavor. We prove that they exhibit a sharp exponential volume growth, are non-Liouville, and that the simple random walk on them has positive speed almost surely. We conjectu...
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作者：Eberle, Andreas
作者单位：University of Bonn
摘要：We consider contractivity for diffusion semigroups w.r.t. Kantorovich ( Wasserstein) distances based on appropriately chosen concave functions. These distances are inbetween total variation and usual Wasserstein distances. It is shown that by appropriate explicit choices of the underlying distance, contractivity with rates of close to optimal order can be obtained in several fundamental classes of examples where contractivity w.r.t. standard Wasserstein distances fails. Applications include ov...
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作者：Barlow, Martin; Burdzy, Krzysztof; Timar, Adam
作者单位：University of British Columbia; University of Washington; University of Washington Seattle; Szeged University
摘要：We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold.
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作者：Chang, Yinshan; Sapozhnikov, Artem
作者单位：Max Planck Society
摘要：We are interested in the clusters formed by a Poisson ensemble of Markovian loops on infinite graphs. This model was introduced and studied in Le Jan (C R Math Acad Sci Paris 350(13-14):643-646, 2012, Ill J Math 57(2):525-558, 2013). It is a model with long range correlations with two parameters and . The non-negative parameter measures the amount of loops, and plays the role of killing on vertices penalizing () or favoring () appearance of large loops. It was shown in Le Jan (Ill J Math 57(2)...
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作者：Teixeira, Augusto
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper we establish some relations between percolation on a given graph G and its geometry. Our main result shows that, if G has polynomial growth and satisfies what we call the local isoperimetric inequality of dimension , then . This gives a partial answer to a question of Benjamini and Schramm (Electron Commun Probab 1(8):71-82 1996). As a consequence of this result and Haggstrom (Adv Appl Probab 32(1):39-66 2000) we derive, that these graphs also undergo a non-trivial phase transiti...
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作者：Iyer, Gautam; Novikov, Alexei
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on intermediate time scales before diffusion sets in. Various heuristics suggest that an anomalous diffusive behaviour should be observed. We prove that the variance on intermediate time scales grows like . Hence, on these time scales the effective behaviour can not be purely diffusive, and is consistent with an anom...
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作者：Dias, J. C. A.; Friedli, S.
作者单位：Universidade Federal de Minas Gerais
摘要：We take a closer look at a class of chains with complete connections introduced by Berger, Hoffman and Sidoravicius. In particular, besides giving a sharper description of the uniqueness and non-uniqueness regimes, we show that if the pure majority rule used to fix the dependence on the past is replaced with a function that is Lipschitz at the origin, then uniqueness always holds, even with arbitrarily slow decaying variation.
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作者：Tsai, Li-Cheng
作者单位：Stanford University
摘要：In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional stochastic differential equation (SDE) corresponding to the bulk limit of Dyson's Brownian Motion, for all . Our construction applies to an explicit and general class of initial conditions, including the lattice configuration and the sine process. We further show the convergence of the finite to infinite-dimensional SDE. This convergence concludes the determinantal formula of Katori and Tanemura (...
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作者：Oliveira, Roberto Imbuzeiro
摘要：Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the lower tail of such a matrix, and prove that it is sub-Gaussian under a simple fourth moment assumption on the one-dimensional marginals of the random vectors. A similar result holds for more general sums of random positive semidefinite matrices, and our (relatively simple) proof uses a variant of the so-called PAC-Bayesian method for bounding empirical processes. Us...
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作者：Knapik, B. T.; Szabo, B. T.; van der Vaart, A. W.; van Zanten, J. H.
作者单位：Vrije Universiteit Amsterdam; Budapest University of Technology & Economics; Leiden University - Excl LUMC; Leiden University; University of Amsterdam
摘要：We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed in automatically selecting this parameter optimally, resulting in optimal convergence rates for truths with Sobolev or analytic smoothness, without using knowledge about this regularity. Both method...
