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作者：Crisan, Dan; McMurray, Eamon
作者单位：Imperial College London
摘要：In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives...
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作者：Zhang, Yu
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We independently assign a non-negative value, as a capacity for the quantity of flows per unit time, with a distribution F to each edge on the lattice. We consider the maximum flows through the edges from a source to a sink in a large cube. In this paper, we show that the ratio of the maximum flow and the size of the source is asymptotic to a constant. This constant is denoted by the flow constant. By the max-flow and min-cut theorem, this is equivalent to a statement about the asymptotic beha...
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作者：Duminil-Copin, H.; Tassion, V.; Teixeira, A.
作者单位：Universite Paris Saclay; University of Geneva
摘要：We consider critical oriented Bernoulli percolation on the square lattice . We prove a Russo-Seymour-Welsh type result which allows us to derive several new results concerning the critical behaviorWe establish that the probability that the origin is connected to distance n decays polynomially fast in n. We prove that the critical cluster of 0 conditioned to survive to distance n has a typical width satisfying for some . The sub- linear polynomial fluctuations contrast with the supercritical re...
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作者：Budzinski, Thomas
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We introduce and study a new random surface, which we call the hyperbolic Brownian plane and which is the near-critical scaling limit of the hyperbolic triangulations constructed by Curien (Probab Theory Relat Fields 165(3):509-540, 2016). The law of the hyperbolic Brownian plane is obtained after biasing the law of the Brownian plane of Curien and Le Gall (J Theoret Probab 27(4):1249-1291, 2014) by an explicit martingale depending on its perimeter and volume processes studied by Curien and Le...
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作者：Collins, Benoit; Dahlqvist, Antoine; Kemp, Todd
作者单位：Kyoto University; Centre National de la Recherche Scientifique (CNRS); University of Cambridge; University of California System; University of California San Diego
摘要：The Brownian motion on the unitary group converges, as a process, to the free unitary Brownian motion as . In this paper, we prove that it converges strongly as a process: not only in distribution but also in operator norm. In particular, for a fixed time , we prove that the unitary Brownian motion has a spectral edge: there are no outlier eigenvalues in the limit. We also prove an extension theorem: any strongly convergent collection of random matrix ensembles independent from a unitary Brown...
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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 ...
