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作者：Seddik, Mohamed El Amine; Guillaud, Maxime; Couillet, Romain
作者单位：Inria; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：Relying on random matrix theory (RMT), this paper studies asymmetric order-d spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of Lim (In Proc. IEEE International Workshop on Computational Advances in Multi -Sensor Adaptive Processing (2005) 129-132), we show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric blockwise random matrix, that is constructed from contractions of the studi...
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作者：Abry, Patrice; Boniece, B. cooper; Didier, Gustavo; Wendt, Herwig
作者单位：Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Drexel University; Tulane University; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices in high dimensions. We assume that possibly non-Gaussian, finite-variance p-variate measurements are made of a low-dimensional r-variate (r << p ) fractional stochastic process with noncanonical scaling coordinates and in the presence of additive high- dimensional noise. The measurements are correlated both timewise and between rows. We show that the r largest eigenvalues of the...
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作者：Broutin, Nicolas; Kamcev, Nina; Ugosi, Gabor
作者单位：Sorbonne Universite; Universite Paris Cite; University of Zagreb; ICREA
摘要：We consider random temporal graphs, a version of the classical Erdos- R & eacute;nyi random graph G(n, p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time stamps. We study the asymptotics for the distances in such graphs, mostly in the regime of interest where np is of order log n. We establish the first order asymptotics for the lengths of increasing paths: the lengths of the shortest and longest paths b...
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作者：Chen, Xinxin; Garban, Christophe; Shekhar, Atul
作者单位：Beijing Normal University; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We give a complete characterization of the domain of attraction of fixed points of branching Brownian motion (BBM) with critical drift. Prior to this classification, we introduce a suitable metric space of locally finite point measures on which we prove 1) that the BBM with critical drift is a well-defined Markov process and 2) that it satisfies the Feller property. Several applications of this characterization are given.
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作者：Cheng, Dan; Xiao, Yimin
作者单位：Arizona State University; Arizona State University-Tempe; Michigan State University
摘要：Let { (X (t), Y(s)) : t is an element of T, s is an element of S } be an R2-valued, centered, unit-variance smooth Gaussian vector field, where T and S are compact rectangles in the Euclidean space. It is shown that, as u -> infinity , the joint excursion probability P{supt is an element of T X (t) >= u, sup s is an element of S Y(s) >= u } can be approximated by E{chi (Au)}, the expected Euler characteristic of the excursion set Au = { (t, s) is an element of T x S : X (t) >= u, Y(s) >= u } ,...
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作者：Banderier, Cyril; Kuba, Markus; Wallner, Michael
作者单位：Universite Paris 13; Technische Universitat Wien; Technische Universitat Wien
摘要：Multitudinous probabilistic and combinatorial objects are associated with generating functions satisfying a composition scheme F(z) = G(H(z)). The analysis becomes challenging when this scheme is critical (i.e., G and H are simultaneously singular). Motivated by many examples (random mappings, planar maps, directed lattice paths), we consider a natural extension of this scheme, namely F(z, u) = G(uH(z))M(z). We also consider a variant of this scheme, which allows us to analyse the number of H-...
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作者：Friesen, Martin; Jin, Peng
作者单位：Dublin City University; Beijing Normal-Hong Kong Baptist University
摘要：The Volterra square-root process on R-+(m) is an affine Volterra process with continuous sample paths. Under a suitable integrability condition on the resolvent of the second kind associated with the Volterra convolution kernel, we establish the existence of limiting distributions. In contrast to the classical square-root diffusion process, here the limiting distributions may depend on the initial state of the process. Our result shows that the nonuniqueness of limiting distributions is closel...
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作者：Qin, Qian
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix algebra exercises. It is found that in terms of asymptotic variance, the two-component random-scan Gibbs sampler is never much worse, and could be considerably better than its deterministic-scan counterpart, provided that the selection probability is appropriately...
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作者：Roberts, Asher
作者单位：City University of New York (CUNY) System
摘要：In this paper we quantify the rate of convergence in Selberg's central limit theorem for log |zeta (1/2 + it)| based on the method of proof given by the same rate of convergence of (log log log T )2/root log log T as Selberg in (In 1989) Univ (1992) 367-385) in the Kolmogorov distance by using the Dudley distance instead. We also prove the theorem for the multivariate case given by same rate of convergence as in the single variable case.
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作者：Ziliotto, Bruno
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：In a zero -sum stochastic game with signals (Repeated Games (2015) Cambridge Univ. Press, Chapter IV), at each stage, two adversary players make decisions and receive stage payoffs determined by these decisions and a variable called the state. The state follows a Markov chain controlled by both players. Actions and states are imperfectly observed by players, who receive private signals at each stage. Mertens (In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, ...
