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作者：Aidekon, Elie; de Raphelis, Loic
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We show that the trace of the null recurrent biased random walk on a Galton-Watson tree properly renormalized converges to the Brownian forest. Our result extends to the setting of the random walk in random environment on a Galton-Watson tree.
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作者：Baudoin, Fabrice; Wang, Jing
作者单位：University of Connecticut; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces and . The characteristic functions of those processes are computed and limit theorems are obtained. In the case , we also study windings of the Brownian motion on those spaces and compute the limit distributions. For the geometry of the Hopf fibration plays a central role, whereas for it is the anti-de Sitter fibration.
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作者：Cook, Nicholas A.
作者单位：University of California System; University of California Los Angeles
摘要：We prove that the (non-symmetric) adjacency matrix of a uniform random d-regular directed graph on n vertices is asymptotically almost surely invertible, assuming for a sufficiently large constant . The proof makes use of a coupling of random regular digraphs formed by shuffling the neighborhood of a pair of vertices, as well as concentration results for the distribution of edges, proved in Cook (Random Struct Algorithms. 2014). We also apply our general approach to prove asymptotically almost...
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作者：Klopp, Olga; Lounici, Karim; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite Paris Saclay; University System of Georgia; Georgia Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Institut Polytechnique de Paris; ENSAE Paris
摘要：This paper considers the problem of estimation of a low-rank matrix when most of its entries are not observed and some of the observed entries are corrupted. The observations are noisy realizations of a sum of a low-rank matrix, which we wish to estimate, and a second matrix having a complementary sparse structure such as elementwise sparsity or columnwise sparsity. We analyze a class of estimators obtained as solutions of a constrained convex optimization problem combining the nuclear norm pe...
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作者：Bhamidi, Shankar; Dey, Partha S.; Nobel, Andrew B.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Illinois System; University of Illinois Urbana-Champaign
摘要：The problem of finding large average submatrices of a real-valued matrix arises in the exploratory analysis of data from a variety of disciplines, ranging from genomics to social sciences. In this paper we provide a detailed asymptotic analysis of large average submatrices of an Gaussian random matrix. The first part of the paper addresses global maxima. For fixed k we identify the average and the joint distribution of the submatrix having largest average value. As a dual result, we establish ...
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作者：Budhiraja, Amarjit; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas the second describes a collection of pure jump Markov processes with a countable state space. For both cases the moderate deviation principle is formulated in terms of a large deviation principle (LDP), with an appropriate speed function, for suitably centered...
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作者：Subag, Eliran; Zeitouni, Ofer
摘要：Recently, sharp results concerning the critical points of the Hamiltonian of the p-spin spherical spin glass model have been obtained by means of moments computations. In particular, these moments computations allow for the evaluation of the leading term of the ground-state, i.e., of the global minimum. In this paper, we study the extremal point process of critical points-that is, the point process associated to all critical values in the vicinity of the ground-state. We show that the latter c...
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作者：Fitzner, Robert; van der Hofstad, Remco
作者单位：Eindhoven University of Technology
摘要：The lace expansion is a powerful perturbative technique to analyze the critical behavior of random spatial processes such as the self-avoiding walk, percolation and lattice trees and animals. The non-backtracking lace expansion (NoBLE) is a modification that allows us to improve its applicability in the nearest-neighbor setting on the -lattice for percolation, lattice trees and lattice animals. The NoBLE gives rise to a recursive formula that we study in this paper at a general level. We state...
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作者：Fehrman, Benjamin J.
作者单位：Max Planck Society
摘要：The results of this paper build upon those first obtained by Sznitman and Zeitouni (Invent Math 164(3), 455-567, 2006). We establish, for spacial dimensions , the existence of a unique invariant measure for isotropic diffusions in random environment on which are small perturbations of Brownian motion. Furthermore, we establish a general homogenization result for initial data which are locally measurable with respect to the coefficients.
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作者：Belius, David; Kistler, Nicola
作者单位：New York University; Goethe University Frankfurt
摘要：The -cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance from any point. Its leading order in the small -regime has been established by Dembo et al. (Ann Math 160:433-464, 2004). In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.
