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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：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：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：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：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...
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作者：Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Royal Institute of Technology; Institute of Science & Technology - Austria
摘要：We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the ErdAs-R,nyi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy-Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency ma...
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作者：Deuschel, Jean-Dominique; Tuan Anh Nguyen; Slowik, Martin
作者单位：Technical University of Berlin
摘要：We consider a stationary and ergodic random field that is parameterized by the edge set of the Euclidean lattice , . The random variable , taking values in and satisfying certain moment bounds, is thought of as the conductance of the edge e. Assuming that the set of edges with positive conductances give rise to a unique infinite cluster , we prove a quenched invariance principle for the continuous-time random walk among random conductances under certain moment conditions. An essential ingredie...
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作者：Joos, Felix; Perarnau, Guillem; Rautenbach, Dieter; Reed, Bruce
作者单位：University of Birmingham; Ulm University; Centre National de la Recherche Scientifique (CNRS); Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：For a fixed degree sequence , let be a uniformly chosen (simple) graph on where the vertex i has degree . In this paper we determine whether has a giant component with high probability, essentially imposing no conditions on . We simply insist that the sum of the degrees in which are not 2 is at least for some function going to infinity with n. This is a relatively minor technical condition, and when does not satisfy it, both the probability that has a giant component and the probability that h...
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作者：Najnudel, Joseph
作者单位：University System of Ohio; University of Cincinnati
摘要：In the present paper, we show that under the Riemann hypothesis, and for fixed h, epsilon > 0, the supremum of the real and the imaginary parts of log.(1/ 2 + i t) for t. [ UT -h, UT + h] are in the interval [(1 -epsilon) log log T, (1 + epsilon) log log T] with probability tending to 1 when T goes to infinity, U being a uniform random variable in [ 0, 1]. This proves a weak version of a conjecture by Fyodorov, Hiary and Keating, which has recently been intensively studied in the setting of ra...
