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作者：Chevyrev, Ilya
作者单位：University of Oxford
摘要：We consider random walks and Levy processes in a homogeneous group G. For all p > 0, we completely characterise (almost) all G-valued Levy processes whose sample paths have finite p-variation, and give sufficient conditions under which a sequence of G-valued random walks converges in law to a Levy process in p-variation topology. In the case that G is the free nilpotent Lie group over R-d, so that processes of finite p-variation are identified with rough paths, we demonstrate applications of o...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We discuss subordination of random compact -trees. We focus on the case of the Brownian tree, where the subordination function is given by the past maximum process of Brownian motion indexed by the tree. In that particular case, the subordinate tree is identified as a stable L,vy tree with index 3/2. As a more precise alternative formulation, we show that the maximum process of the Brownian snake is a time change of the height process coding the L,vy tree. We then apply our results to properti...
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作者：Forman, Noah; Haulk, Chris; Pitman, Jim
作者单位：University of Washington; University of Washington Seattle; Alphabet Inc.; Google Incorporated; University of California System; University of California Berkeley
摘要：A hierarchy on a set S, also called a total partition of S, is a collectionHof subsets of S such that S. H, each singleton subset of S belongs toH, and if A, B. H then An B equals either A or B orO. Every exchangeable random hierarchy of positive integers has the same distribution as a random hierarchyHassociated as follows with a random real tree T equipped with root element 0 and a random probability distribution p on the Borel subsets of T : given ( T, p), let t1, t2,... be independent and ...
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作者：Rezaei, Mohammad A.; Zhan, Dapeng
作者单位：Michigan State University
摘要：For a chordal SLE () curve in a domain D, the n-point Green's function valued at distinct points is defined to be here is the Hausdorff dimension of SLE, provided that the limit converges. In this paper, we will show that such Green's functions exist for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give up-to-constant bounds for them.
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作者：Wang, Zhenan
作者单位：University of Washington; University of Washington Seattle
摘要：Under general conditions we show an a priori probabilistic Harnack inequality for the non-negative solution of a stochastic partial differential equation of the following form We also show that the solutions of the above equation are almost surely strictly positive if the initial condition is non-negative and not identically vanishing.
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作者：Hermon, Jonathan; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：There are several works characterizing the total-variation mixing time of a reversible Markov chain in term of natural probabilistic concepts such as stopping times and hitting times. In contrast, there is no known analog for the L-2 mixing time, tau(2) (while there are sophisticated analytic tools to bound tau(2), in general they do not determine tau(2) up to a constant factor and they lack a probabilistic interpretation). In this work we show that tau(2) can be characterized up to a constant...
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作者：Beliaev, Dmitry; Wigman, Igor
作者单位：University of Oxford; University of London; King's College London
摘要：We study the volume distribution of nodal domains of families of naturally arising Gaussian random fields on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.
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作者：De, Anindya; Servedio, Rocco A.
作者单位：Northwestern University; Columbia University
摘要：One of the main results of this paper is a new multidimensional central limit theorem (CLT) for multivariate polynomials under Gaussian inputs. Roughly speaking, the new CLT shows that any collection of Gaussian polynomials with small eigenvalues (suitably defined) must have a joint distribution which is close to a multidimensional Gaussian distribution. The new CLT is proved using tools from Malliavin calculus and Stein's method. A second main result of the paper, which complements the new CL...
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作者：Bordenave, Charles; Caputo, Pietro; Salez, Justin
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Roma Tre University; Universite Paris Cite
摘要：A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the context of card shuffling (Aldous and Diaconis in Am Math Mon 93:333-348, 1986), this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse directed graphs, for whi...
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作者：Coca, Alberto J.
作者单位：University of Cambridge
摘要：A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L,vy distributions are proposed and functional central limit theorems using the uniform norm are proved for both under mild conditions. The limiting Gaussian processes are identified and efficiency of the estimators is established. Kernel estimators for the mass function, the intensity and the drift are also proposed, their asymptotic properties in...
