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作者：Baccelli, Francois; Haji-Mrsadeghi, Mir -Omid; Haniha, Sayeh k
作者单位：Inria; Sharif University of Technology
摘要：The Doeblin graph of a countable state space Markov chain describes the joint pathwise evolutions of the Markov dynamics starting from all possible initial conditions, with two paths coalescing when they reach the same point of the state space at the same time. Its bridge Doeblin subgraph only contains the paths starting from a tagged point of the state space at all possible times. In the irreducible, aperiodic, and positive recurrent case, the following results are known: the bridge Doeblin g...
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作者：Bensoussan, Alain; Graber, P. Jameson; Yam, Sheung Chi Phillip
作者单位：University of Texas System; University of Texas Dallas; Baylor University; Chinese University of Hong Kong
摘要：We propose a new approach to studying classical solutions of the second order Bellman equation and master equation for mean field type control problems, using a novel form of the lifting idea introduced by P.-L. Lions. Rather than studying the usual system of Hamilton-Jacobi/Fokker-Planck PDEs using analytic techniques, we instead study a stochastic control problem on a specially constructed Hilbert space, which is reminiscent of a tangent space on the Wasserstein space in optimal transport. O...
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作者：Bruned, Yvain; Nadeem, Usama
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; University of Edinburgh; Heriot Watt University
摘要：In this work, we show a convergence result for the discrete formulation of the generalised KPZ equation Bt u = (Au) +g(u)(Vu)2 +k(Vu) +h(u) + f (u)xi t(x), where xi is real -valued, A is the discrete Laplacian, and V is a discrete gradient, without fixing the spatial dimension. Our convergence result is established within the discrete regularity structures introduced by Hairer and Erhard (Ann. Inst. Henri Poincare Probab. Stat. 55 (2019) 2209-2248). We extend with new ideas the convergence res...
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作者：Wolfer, Geoffrey; Kontorovich, Aryeh
作者单位：RIKEN; Ben-Gurion University of the Negev
摘要：We show that the minimax sample complexity for estimating the pseudo spectral gap gamma(ps) of an ergodic Markov chain in constant multiplicative error is of the order of (Theta) over tilde (1/gamma(ps)pi(star)), where pi(star) is the minimum stationary probability, recovering the known bound in the reversible setting for estimating the absolute spectral gap (Hsu et al., Ann. Appl. Probab. 29 (2019) 2439-2480), and resolving an open problem of Wolfer and Kontorovich (In Proceedings of the Thir...
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作者：Bayraktar, Erhan; Guo, Gaoyue; Tang, Wenpin; Zhang, Yuming Paul
作者单位：University of Michigan System; University of Michigan; Universite Paris Saclay; Universite Paris Saclay; Columbia University; University of California System; University of California San Diego
摘要：This paper is concerned with the analysis of blow-ups for two McKean-Vlasov equations involving hitting times. Let (B(t); t >= 0) be standard Brownian motion, and tau := inf{t >= 0 : X(t) <= 0} be the hitting time to zero of a given process X. The first equation is X(t) = X(0-) + B(t) - alpha P(tau <= t). We provide a simple condition on a and the distribution of X(0-) such that the corresponding Fokker-Planck equation has no blow-up, and thus the McKean-Vlasov dynamics is well defined for all...
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作者：Ferrari, Patrik; Occelli, Alessandra
作者单位：University of Bonn; Universite d'Angers
摘要：This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first-order correction to the covariance for the point-to-point model is the same as the one of the stationary model. In order to obtain the result, we first derive comparison inequalities of the last passage increments for different models. This is used to prove tightness of the point-to-poi...
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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.
