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作者：Wang, Feng-Yu
作者单位：Tianjin University
摘要：In terms of a nice reference probability measure, integrability conditions on the path-dependent drift are presented for (infinite-dimensional) degenerate PDEs to have regular positive solutions. To this end, the corresponding stochastic (partial) differential equations are proved to possess the weak existence and uniqueness of solutions, as well as the existence, uniqueness and entropy estimates of invariant probability measures. When the reference measure satisfies the log-Sobolev inequality...
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作者：Qian, Wei
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The study of conformal restriction properties in two-dimensions has been initiated by Lawler et al. (J Am Math Soc 16(4):917-955, 2003) who focused on the natural and important chordal case: they characterized and constructed all random subsets of a given simply connected domain that join two marked boundary points and that satisfy the additional restriction property. The radial case (sets joining an inside point to a boundary point) has then been investigated by Wu (Stoch Process Appl 125(2):...
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作者：Berestycki, J.; Fittipaldi, M. C.; Fontbona, J.
作者单位：University of Oxford; Universidad Nacional Autonoma de Mexico; Universidad de Chile; Universidad de Chile
摘要：We introduce flows of branching processes with competition, which describe the evolution of general continuous state branching populations in which interactions between individuals give rise to a negative density dependence term. This generalizes the logistic branching processes studied by Lambert (Ann Appl Probab 15(2):1506-1535, 2005). Following the approach developed by Dawson and Li (Ann Probab 40(2):813-857, 2012), we first construct such processes as the solutions of certain flow of stoc...
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作者：Berestycki, Nathanael; Webb, Christian; Wong, Mo Dick
作者单位：University of Cambridge; Aalto University
摘要：We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary invariant ensembles, converge in law to Gaussian multiplicative chaos measures. We prove this in the so-called L2-phase of multiplicative chaos. Our main tools are asymptotics of Hankel determinants with Fisher-Hartwig singularities. Using Riemann-Hilbert methods, we prove a rather general Fisher-Hartwig formula for ...
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作者：He, Yukun; Knowles, Antti; Rosenthal, Ron
作者单位：University of Geneva; Technion Israel Institute of Technology
摘要：We present a simple and versatile method for deriving (an)isotropic local laws for general random matrices constructed from independent random variables. Our method is applicable to mean-field random matrices, where all independent variables have comparable variances. It is entirely insensitive to the expectation of the matrix. In this paper we focus on the probabilistic part of the proof-the derivation of the self-consistent equations. As a concrete application, we settle in complete generali...
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作者：Zhai, Alex
作者单位：Stanford University
摘要：Let X-1, ... , X-n be i.i.d. random vectors in R-d with parallel to X-1 parallel to <= beta. Then, we show that 1/root n (X-1 + ... + X-n) converges to a Gaussian in quadratic transportation (also known as Kantorovich or Wasserstein) distance at a rate of O(root d beta log n/root n), improving a result of Valiant and Valiant. The main feature of our theorem is that the rate of convergence is within log n of optimal for n, d -> infinity.
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作者：Chen, Le; Hu, Yaozhong; Kalbasi, Kamran; Nualart, David
作者单位：University of Kansas; University of Warwick
摘要：This paper studies the stochastic heat equation driven by time fractional Gaussian noise with Hurst parameter . We establish the Feynman-Kac representation of the solution and use this representation to obtain matching lower and upper bounds for the moments of the solution.
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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 ...
