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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：Callegaro, Alice; Roberts, Matthew I.
作者单位：Technical University of Munich; University of Bath
摘要：We define a fragmentation process which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin rectangles are more likely to break quickly, whereas squares break more slowly. Each rectangle is also more likely to split along its longest side. We are interested in how the system evolves over time: how many fragments are there of different shapes and sizes, and how did they reach that state? Using a standard transformation this fragmenta...
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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：Jiao, Yong; Osekowski, Adam; Wu, Lian
作者单位：Central South University; University of Warsaw
摘要：We introduce the notion of differential subordination in the context of noncommutative continuous-time martingales and show that for 2 < infinity this domination enforces the corresponding L-p bound between the two processes. As applications, we obtain best-order L-p inequalities for the second-order Riesz transforms on a class of group von Neumann algebras equipped with a conditionally negative length function. The proof relies on a novel stochastic representation of these second-order operat...
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作者：Cannizzaro, Giuseppe; Giles, Harry
作者单位：University of Warwick
摘要：We investigate the large-scale behaviour of the Self-Repelling Brownian Polymer (SRBP) in the critical dimension d=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=2$$\end{document}. The SRBP is a model of self-repelling motion, which is formally given by the solution to a stochastic differential equation driven ...
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作者：Bao, Zhigang; Cipolloni, Giorgio; Erdos, Laszlo; Henheik, Joscha; Kolupaiev, Oleksii
作者单位：University of Hong Kong; University of Arizona; Institute of Science & Technology - Austria
摘要：We consider the Wigner minor process, i.e. the eigenvalues of an NxN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\times N$$\end{document} Wigner matrix H(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
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作者：Avena, Luca; van der Hofstad, Remco; den Hollander, Frank; Nagy, Oliver
作者单位：University of Florence; Eindhoven University of Technology; Leiden University; Leiden University - Excl LUMC
摘要：We analyse the mixing profile of a random walk on a dynamic random permutation, focusing on the regime where the walk evolves much faster than the permutation. Two types of dynamics generated by random transpositions are considered: one allows for coagulation of permutation cycles only, the other allows for both coagulation and fragmentation. We show that for both types, after scaling time by the length of the permutation and letting this length tend to infinity, the total variation distance b...
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作者：Scardia, Lucia; Zemas, Konstantinos; Zeppieri, Caterina Ida
作者单位：Heriot Watt University; University of Bonn; University of Munster
摘要：In this paper we study the convergence of nonlinear Dirichlet problems for systems of variational elliptic PDEs defined on randomly perforated domains of R-n. Under the assumption that the perforations are small balls whose centres and radii are generated by a stationary short-range marked point process, we obtain in the critical-scaling limit an averaged nonlinear analogue of the extra term obtained in the classical work of Cioranescu and Murat (Res Notes Math III, 1982). In analogy to the ra...
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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：Enriquez, Nathanael; Liu, Mike; Menard, Laurent; Perchet, Vianney
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the limiting tree. For this purpose, we introduce and study unimodular matchings on weighted unimodular random trees as well as a notion of optimality for these objects. In this context, we prove that, in law, there is a unique optimal unimodular matching for a give...
