-
作者：Grazieschi, P.; Matetski, K.; Weber, H.
作者单位：University of Bath; Michigan State University; University of Munster
摘要：We consider the Glauber dynamics of a ferromagnetic Ising-Kac model on a three-dimensional periodic lattice of size (2N + 1)(3), in which the flipping rate of each spin depends on an average field in a large neighborhood of radius gamma(-1 )<< N. We study the random fluctuations of a suitably rescaled coarse-grained spin field as N -> infinity and gamma -> 0; we show that near the mean-field value of the critical temperature, the process converges in distribution to the solution of the dynamic...
-
作者：Montanari, Andrea; Wein, Alexander S.
作者单位：Stanford University; Stanford University; University of California System; University of California Davis
摘要：We consider the problem of estimating an unknown parameter vector theta is an element of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\theta }}\in {{\mathbb {R}}}<^>n$$\end{document}, given noisy observations Y=theta theta T/n+Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \u...
-
作者：Michelen, Marcus; Yakir, Oren
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Tel Aviv University
摘要：Smale's Seventh Problem asks for an efficient algorithm to generate a configuration of n points on the sphere that nearly minimizes the logarithmic energy. As a candidate starting configuration for this problem, Armentano, Beltr & aacute;n and Shub considered the set of points given by the stereographic projection of the roots of the random elliptic polynomial of degree n and computed the expected logarithmic energy. We study the fluctuations of the logarithmic energy associated to this random...
-
作者：Wu, Wei
作者单位：New York University; NYU Shanghai
摘要：We consider the gradient field model in -N,N2 boolean AND Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left[ -N,N\right] <^>{2}\cap {\mathbb {Z}}<^>{2}$$\end{document} with a uniformly convex interaction potential. Naddaf-Spencer (Comm Math Phys 183(1):55-84, 1997) and Miller (Comm Math Phys 908(3):591-639, 2...
-
作者：Herry, Ronan; Malicet, Dominique; Poly, Guillaume
作者单位：Universite de Rennes; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We study the regularity of the law of a quadratic form Q(X, X), evaluated in a sequence X = ( Xi) of independent and identically distributed random variables, when X1 can be expressed as a sufficiently smooth function of a Gaussian field. This setting encompasses a large class of important and frequently used distributions, such as, among others, Gaussian, Beta, for instance uniform, Gamma distributions, or else any polynomial transform of them. Let us present an emblematic application. Take X...
-
作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Geneva; Imperial College London
摘要：For a large class of amenable transient weighted graphs G, we prove that the sign clusters of the Gaussian free field on G fall into a regime of strong supercriticality, in which two infinite sign clusters dominate (one for each sign), and finite sign clusters are necessarily tiny, with overwhelming probability. Examples of graphs belonging to this class include regular lattices such as Z d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...
