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作者：Banerjee, Sayan; Budhiraja, Amarjit
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Consider an infinite collection of particles on the real line moving according to independent Brownian motions and such that the i-th particle from the left gets the drift gi-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{i-1}$$\end{document}. The case where g0=1\documentclass[12pt]{minimal} \usepackage{amsmat...
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作者：Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia
作者单位：University of Strathclyde; Utah System of Higher Education; University of Utah; Pompeu Fabra University
摘要：We consider the following stochastic heat equation partial derivative(t)u(t,x)=1/2 partial derivative(2)(x)u(t,x)+b(u(t,x))+sigma(u(t,x)) W(t,x), defined for (t,x)is an element of(0,infinity)xR, where Wdenotes space-time white noise. The function sigma is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly awayfrom the origin, and the function b is assumed to be positive, locally Lipschitz and non decreasing. We prove that the Os good condition integral infinity 1dyb(y)0...
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作者：Murugan, Mathav
作者单位：University of British Columbia
摘要：We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of Jones (Acta Math 147(1-2):71-88, 1981) states that uniform domains in Euclidean space are extension domains for Sobolev spaces. In this work, we obtain a similar extension property for metric spaces equipped with a Dirichlet form whose heat kernel satisfies a sub-Gaussian estimate. We introduce a scale-invariant versi...
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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：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...
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作者：Berger, Quentin; Legrand, Alexandre
作者单位：Sorbonne Universite; Universite Paris Cite; Universite PSL; Ecole Normale Superieure (ENS); Institut Universitaire de France; 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; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The Poland-Scheragamodel, introduced in the 1970s, is a reference model to describe the denaturation transition of DNA. More recently, it has been generalized in order to allow for asymmetry in the strands lengths and in the formation of loops: the mathematical representation is based on a bivariate renewal process, that describes the pairs of bases that bond together. Here, we consider a disordered version of the model, in which the two strands interact via a potential ss V ( . i, . j) + h wh...
