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作者：Lecue, Guillaume; Shang, Zong
作者单位：ESSEC Business School; Institut Polytechnique de Paris; Ecole Polytechnique; ENSAE Paris
摘要：In the linear regression model, the minimum 2-norm interpolant estimator ss has received much attention since it was proved to be consistent even though it fits noisy data perfectly under some condition on the covariance matrix of the input vector, known as benign overfitting. Motivated by this phenomenon, we study the generalization property of this estimator from a geometrical viewpoint. Our main results extend and improve the convergence rates as well as the deviation probability from (Tsig...
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作者：Chen, Hong-Bin; Xia, Jiaming
作者单位：New York University; University of Pennsylvania
摘要：We give a meaning to the Hamilton-Jacobi equation arising from mean-field spin glass models in the viscosity sense, and establish the corresponding well-posedness. Originally defined on the set of monotone probability measures, these equations can be interpreted, via an isometry, to be defined on an infinite-dimensional closed convex cone with an empty interior in a Hilbert space. We prove the comparison principle, and the convergence of finite-dimensional approximations furnishing the existen...
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作者：Pene, Francoise; Saussol, Benoit
作者单位：Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We are interested in the study of the asymptotic behaviour of return times in small balls for the T, T-1-transformation. We exhibit different asymptotic behaviour (different scaling, different limit point process) depending on the respective dimensions of the measures of the two underlying dynamical systems. It behaves either as for the direct product of the underlying systems, or as for the Z-extension of the driving system (also studied in this article), or as a more sophisticated process.
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作者：Narayanan, Hariharan; Rajaraman, Amit; Srivastava, Piyush
作者单位：Tata Institute of Fundamental Research (TIFR); Massachusetts Institute of Technology (MIT)
摘要：A standard approach for sampling approximately uniformly from a convex body K subset of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K \subseteq \mathbb {R}<^>n$$\end{document} is to run a random walk within K. The requirement is that starting from a suitable initial distribution, the random walk should mix ra...
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作者：Grazieschik, P.; Matetski, K.; Weber, H.
作者单位：University of Bath; Michigan State University; University of Munster
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作者：Sly, Allan; Sohn, Youngtak
作者单位：Princeton University; Massachusetts Institute of Technology (MIT)
摘要：The local behavior of typical solutions of random constraint satisfaction problems (CSP) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the constraint density is low, studying the planted model is a powerful technique for determining this local behavior which in many examples has a simple Markovian structure. The work of Coja-Oghlan, Kapetanopoulos, Muller (Comb Prob Comput 29:346-422, 2020) showed...
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作者：Gabriel, Simon; Rosati, Tommaso; Zygouras, Nikos
作者单位：University of Munster; University of Warwick
摘要：This work considers the two-dimensional Allen-Cahn equation partial derivative tu=12 Delta u+mu-u3,u(0,x)=eta(x),for all(t,x)is an element of[0,infinity)xR2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t u = \frac{1}{2}\Delta u + \mathfrak {m}\, u -u<^>3, \quad u(0,x)= \eta (x), \qquad ...
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作者：Roeckner, Michael; Zhao, Guohuan
作者单位：University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This paper is a continuation of (R & ouml;ckner and Zhao, Bernoulli 29(1), 821 757-784 (2023)). Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces, which gives an affirmative answer to a longstanding open problem. As an application, we also prove a regularity criterion for solutions of a stochastic system proposed b...
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作者：Das, Sayan; Zhu, Weitao
作者单位：Columbia University
摘要：We consider the continuum directed random polymer (CDRP) model that arises as a scaling limit from 1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document} dimensional directed polymers in the intermediate disorder regime. We show that for a point-to-point polymer of length t and any p is an element o...
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作者：Blanca, Antonio; Gheissari, Reza
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Northwestern University
摘要：Sampling from the q-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem may be computationally hard, and this hardness holds at arbitrarily low temperatures. At the same time, in recent years, there has been significant progress showing the existence of low-temperature sampling algorithms in various specific families of graphs. Our aim in this paper is to understand the minimal s...
