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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
摘要：We study the growth and isoperimetry of infinite clusters in slightly supercritical Bernoulli bond percolation on transitive nonamenable graphs under the L-2 boundedness condition (p(c) < p(2 -> 2)). Surprisingly, we find that the volume growth of infinite clusters is always purely exponential (that is, the subexponential corrections to growth are bounded) in the regime p(c) < p < p(2 -> 2), even when the ambient graph has unbounded corrections to exponential growth. For p slightly larger than...
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作者：Hotz, Thomas; Le, Huiling; Wood, Andrew T. A.
作者单位：Technische Universitat Ilmenau; University of Nottingham; Australian National University
摘要：We prove a central limit theorem (CLT) for the Fr & eacute;chet mean of independent and identically distributed observations in a compact Riemannian manifold assuming that the population Fr & eacute;chet mean is unique. Previous general CLT results in this setting have assumed that the cut locus of the Fr & eacute;chet mean lies outside the support of the population distribution. In this paper we present a CLT under some mild technical conditions on the manifold plus the following assumption o...
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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：Chhor, Julien; Sigalla, Suzanne; Tsybakov, Alexandre B.
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Institut Polytechnique de Paris; Ecole Polytechnique; ENSAE Paris
摘要：We study benign overfitting in the setting of nonparametric regression under mean squared risk, and on the scale of H & ouml;lder classes. We construct a local polynomial estimator of the regression function that is minimax optimal on a H & ouml;lder class with any given smoothness, and that is a continuous function interpolating the set of observations with high probability. The key element of the construction is the use of singular kernels. Moreover, we prove that adaptation to unknown smoot...
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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：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...
