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作者：Agresti, Antonio; Veraar, Mark
作者单位：Institute of Science & Technology - Austria; Delft University of Technology
摘要：In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under w...
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作者：Huang, Jiaoyang
摘要：In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal concentration estimate for the tiling height functions and arctic boundaries on such domains: with overwhelming probability the tiling height function is within n(delta) of its limit shape, and the tiling arctic boundary is within n(1/3+delta) to its limit shape, for arbitrarily small delta > 0. This concentration resul...
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作者：Jirak, Moritz; Wahl, Martin
作者单位：University of Vienna; University of Bielefeld
摘要：Given finite i.i.d. samples in a Hilbert space with zero mean and trace-class covariance operator Sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document}, the problem of recovering the spectral projectors of Sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackag...
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作者：Huang, Han; Tikhomirov, Konstantin
作者单位：University of Missouri System; University of Missouri Columbia; Carnegie Mellon University
摘要：The Gaussian elimination with partial pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical evidence strongly suggests that for a typical square coefficient matrix, GEPP is numerically stable. We obtain a (partial) theoretical justification of this phenomenon by showing that, given the random n x n \documentclass[12pt]{minimal} \usepackage{amsmath} \use...
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作者：Lygkonis, Dimitris; Zygouras, Nikos
作者单位：University of Warwick
摘要：The Erdos-Taylor theorem (Acta Math Acad Sci Hungar, 1960) states that if L(N )is the local time at zero, up to time 2N, of a two-dimensional simple, symmetric random walk, then pi/logN L(N )converges in distribution to an exponential random variable with parameter one. This can be equivalently stated in terms of the total collision time of two independent simple random walks on the plane. More precisely, if L-N((1-2)) = Sigma(N)(n=1) 1({Sn(1)=Sn(2)}), then pi/logN L-N((1, 2)) converges in dis...
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作者：Qi, Weiwei; Shen, Zhongwei; Yi, Yingfei
作者单位：University of Alberta; Jilin University
摘要：The present paper is devoted to the investigation of an important family of absorbed singular diffusion processes exhibiting long transient dynamics, namely, interesting and important dynamical behaviours over long but finite time scales. We explore the multiscale dynamics by establishing the asymptotic distribution of the normalized extinction time, the asymptotic reciprocal relationship between the mean extinction time and the principal eigenvalue of the generator, and a sophisticated multis...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroder, Dominik
作者单位：Princeton University; Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that the mesoscopic linear statistics Sigma(i)f (n(a)(sigma(i) - z(0))) of the eigenvalues {sigma(i)}(i) of large nxn non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H-0(2) -functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0 < a < 1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a = 0, to cover the e...
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作者：Neufeld, Leonie
作者单位：University of Bielefeld
摘要：We study weighted sums of free identically distributed self-adjoint random variables with weights chosen randomly from the unit sphere and show that the Kolmogorov distance between the distribution of such a weighted sum and Wigner's semicircle law is of order n(-1/2) with high probability. Replacing the Kolmogorov distance by a weaker pseudometric, we obtain a rate of convergence of order n(-1), thus providing a free analog of the Klartag-Sodin result in classical probability theory. Moreover...
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作者：Gouezel, Sebastien; Rousseau, Jerome; Stadlbauer, Manuel
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal da Bahia
摘要：We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical systems (the so-called annealed version of the problem): it is known that the asymptotic behavior for this question is given by a dimension-like quantity associated to the invariant measure, called correlation dimension (or R & eacute;nyi entropy). We s...
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作者：Deuschel, Jean-Dominique; Rodriguez, Pierre-Francois
作者单位：Technical University of Berlin; Imperial College London
摘要：We introduce a natural measure on bi-infinite random walk trajectories evolving in a time-dependent environment driven by the Langevin dynamics associated to a gradient Gibbs measure with convex potential. We derive an identity relating the occupation times of the Poissonian cloud induced by this measure to the square of the corresponding gradient field, which - generically - is not Gaussian. In the quadratic case, we recover a well-known generalization of the second Ray-Knight theorem. We fur...
