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作者：Han, Yi
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Given An:=1n(a(ij)) an nxn symmetric random matrix, with elements above the diagonal given by i.i.d. random variables having mean zero and unit variance. It is known that when limx ->infinity x(4)P(|a(ij)|>x)=0, then fluctuation of the largest eigenvalue of An follows a Tracy-Widom distribution. When the law of aij is regularly varying with index alpha is an element of(0,4), then the largest eigenvalue has a Fr & eacute;chet distribution. An intermediate regime is recently uncovered in Diaconu...
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作者：Fan, Zhou; Wu, Yihong
作者单位：Yale University
摘要：We study a variant of the Sherrington-Kirkpatrick (S-K) spin glass model with external field, where the random symmetric couplings matrix does not consist of i.i.d. entries but is instead orthogonally invariant in law. For sufficiently high temperature, we prove a replica-symmetric formula for the first-order limit of the model free energy. Our analysis is an adaptation of a conditional second-moment-method argument previously introduced by Bolthausen for studying the high-temperature regime o...
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作者：Dembin, Barbara; Garban, Christophe
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Institut Universitaire de France
摘要：We consider the standard first passage percolation model on Z(d) with a distribution G taking two values 0 < a < b. We study the maximal flow through the cylinder [0, n](d-1) x [0, hn] between its top and bottom as well as its associated minimal surface(s). We prove that the variance of the maximal flow is superconcentrated, i.e. in O( n(d-1) /log n), for h >= h(0) (for a large enough constant h(0) = h(0)(a, b)). Equivalently, we obtain that the ground state energy of a disordered Ising ferrom...
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作者：Chak, Martin
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：Given global Lipschitz continuity and differentiability of high enough order on the coefficients in It & ocirc;'s equation, differentiability of associated semigroups, existence of twice differentiable solutions to Kolmogorov equations and weak convergence rates of order one for numerical approximations are known. In this work and against the counterexamples of Hairer et al. (Ann Probab 43(2):468-527, https://doi.org/10.1214/13-AOP838, 2015), the drift and diffusion coefficients having Lipschi...
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作者：Hong, Guixiang; Ricard, Eric
作者单位：Harbin Institute of Technology; Universite de Caen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative L-p-martingales when 1 <= p < 2. The same happens to ergodic averages. The proof consists of some sharp estimates of the distributional function of a sequence of matrices and some non standard transference techniques, which might admit further applications.
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作者：Cao, Shiping; Qiu, Hua
作者单位：University of Washington; University of Washington Seattle; Nanjing University
摘要：We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the 1/k grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.
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作者：Adhikari, Arka; Brennecke, Christian; Xu, Changji; Yau, Horng-Tzer
作者单位：Stanford University; University of Bonn; Harvard University; Harvard University
摘要：We consider general mixed p-spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of order one at sufficiently high temperature. Our proof is based on an iteration scheme relating the spectral gap of the N-spin system to that of suitably conditioned subsystems.
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作者：Barbu, Viorel; Roeckner, Michael
作者单位：Romanian Academy; Alexandru Ioan Cuza University; University of Bielefeld
摘要：This work is concerned with the existence of mild solutions to nonlinear Fokker-Planck equations with fractional Laplace operator ( - Delta ) s \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(- \Delta )<^>s$$\end{document} for s is an element of 1 2 , 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackag...
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作者：Baraud, Yannick
作者单位：University of Luxembourg
摘要：In the Bayes paradigm, given a loss function and an n-sample, we present the construction of a new type of posterior distribution, that extends the classical Bayes one. The loss functions we have in mind are either those derived from the total variation and Hellinger distances or some L-j-ones for j > 1. We prove that, with a probability close to one, this new posterior distribution concentrates its mass in a neighbourhood (for the chosen loss function) of the law of the data, provided that th...
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作者：Liu, Yucheng; Slade, Gordon
作者单位：University of British Columbia
摘要：We give conditions on a real-valued function F on Z(d), for d>2, which ensure that the solution G to the convolution equation (F & lowast;G)(x)=delta(0,x) has Gaussian decay |x|(-(d-2)) for large |x|. Precursors of our results were obtained in the 2000s, using intricate Fourier analysis. In 2022, a very simple deconvolution theorem was proved, but its applicability was limited. We extend the 2022 theorem to remove its limitations while maintaining its simplicity -- our main tools are H & ouml;...
