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作者：Janson, Svante
作者单位：Uppsala University
摘要：Uncover the vertices of a given graph, deterministic or random, in uniformly random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization to a Gaussian process. This problem was studied by Hackl, Panholzer, and Wagner for the case when the graph is a uniformly random labelled tree; we generalize their result to more general graphs, including both other classes of random and non-rand...
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作者：Parraud, Felix; Schnelli, Kevin
作者单位：Royal Institute of Technology
摘要：In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of polynomials evaluated in those matrices. We prove an asymptotic expansion in the inverse of the matrix dimension to any order. Out of this result we deduce new formulas for map enumerations and the microstates free entropy. Our approach is based on the interpolatio...
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作者：Forsstrom, Malin P.; Gantert, Nina; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of {0,1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{0,1\}$$\end{document}-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our main focus ...
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作者：Delarue, Francois; Hammersley, William R. P.
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：The purpose of this work is to provide an explicit construction of a strong Feller semigroup on the space of probability measures over the real line that additionally maps bounded measurable functions into Lipschitz continuous functions, with a Lipschitz constant that blows up in an integrable manner in small time. Our construction relies on a rearranged version of the stochastic heat equation on the circle driven by a coloured noise. Formally, this stochastic equation writes as a reflected eq...
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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...
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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...
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作者：Gheissari, Reza; Lubetzky, Eyal
作者单位：Northwestern University; New York University
摘要：We study Glauber dynamics for the low temperature (2 +1)D Solid-On-Solid model on a box of side-length n with a floor at height 0 (inducing entropic repulsion) and a competing bulk external field lambda pointing down (the prewetting problem). In 1996, Cesi and Martinelli showed that if the inverse-temperature beta is large enough, then along a decreasing sequence of critical points (lambda((k)K beta)(c)(k=0) the dynamics is torpid: its inverse spectral gap is O(1) when lambda is an element of ...
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作者：Choi, Inhyeok
作者单位：Korea Institute for Advanced Study (KIAS)
摘要：Let G be a countable group whose action on a metric space X involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm & uuml;ller space, Culler-Vogtmann Outer space and CAT(0) spaces. We discuss continuity and differentiability of the escape rate of random walks on G. For relatively hyperbolic groups, CAT(-1) groups and CAT(0) cubical groups, we further discuss analyticity of the escape rate. Finally, assuming that the action of G on ...
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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...
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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...
