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作者：Eberle, Andreas; Loerler, Francis
作者单位：University of Bonn
摘要：We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivi...
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作者：Bovier, Anton; Schertzer, Adrien
作者单位：University of Bonn
摘要：20 years ago, Bovier, Kurkova, and L & ouml;we (Ann Probab 30(2):605-651, 2002) proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we improve their results in two ways. First, we extend the range of temperatures to cover the entire regime where the quenched and annealed free energies are known to coincide. Second, we identify the main source of the fluctuatio...
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作者：Feng, Yu; Peltola, Eveliina; Wu, Hao
作者单位：Tsinghua University; Aalto University; University of Bonn
摘要：We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q is an element of [ 1 , 4 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsf...
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作者：Dolera, Emanuele; Favaro, Stefano; Mainini, Edoardo
作者单位：University of Pavia; University of Turin; University of Genoa
摘要：In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination of a local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the ...
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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...
