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作者：He, Yukun; Huang, Jiaoyang; Wang, Chen
作者单位：Fudan University; University of Pennsylvania; City University of Hong Kong
摘要：We consider a class of sparse random matrices, which includes the adjacency matrix of the Erd & odblac;s-R & eacute;nyi graph G(N,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{G}(N,p)$$\end{document}. For N-1+o(1)<= p <= 1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepack...
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作者：Aistleitner, Christoph; Fruhwirth, Lorenz; Hauke, Manuel; Manskova, Maryna
作者单位：Graz University of Technology; University of Passau; Norwegian University of Science & Technology (NTNU)
摘要：In a recent paper, Aistleitner, Gantert, Kabluchko, Prochno and Ramanan studied large deviation principles (LDPs) for lacunary trigonometric sums Sigma(N)(K=1 )cos(2 pi n(k)x), where the sequence (n(k)) k >= 1 satisfies the Hadamard gap condition n(k+1)/nk >= q >1 for k >= 1. A crucial ingredient in their work were asymptotic estimates for the moment generating function (MGF) of such sums, which turned out to depend on the fine arithmetic structure of the sequence (n(k)) k >= 1 in an intricate...
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作者：Hip, Andres A. Contreras; Gwynne, Ewain
作者单位：University of Chicago
摘要：We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we study asymptotics for the discrete curvature of & varepsilon;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength...
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作者：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva
摘要：This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions d > 4. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. A companion paper proposes a similar analysis for spread-out Bernoulli percolation in dimensions d > 6 [10].
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作者：Benaim, Michel; Tough, Oliver
作者单位：University of Neuchatel; University of Bath
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作者：Hou, Haojie; Zhang, Xicheng
作者单位：Nankai University; Beijing Institute of Technology; Shenzhen MSU-BIT University
摘要：We use probabilistic techniques to derive sharp and explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator where Delta v alpha/2 denotes the fractional Laplacian acting on the velocity variable v . We also establish logarithmic gradient estimates with respect to both the spatial variable x and the velocity variable v . In fact, our estimates are obtained for more general nonsymmetric stable-like operators and make the dependence on the lower and upper bounds of the k...
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作者：Avraham-Re'em, Nachi; Roy, Emmanuel
作者单位：Technion Israel Institute of Technology; Universite Paris 13
摘要：We prove that for an arbitrary indexing group, every ergodic infinitely divisible stationary process that is separable in probability is weakly mixing. This shows that, as in the well-known case of Gaussian stationary processes, ergodicity implies weak mixing is intrinsic to infinite divisibility, removing all structural assumptions on the group from prior results. The main ingredient is a general construction of stochastically continuous extensions for separable in probability stationary proc...
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作者：Arizmendi, Octavio; Hasebe, Takahiro; Kitagawa, Yu
作者单位：Hokkaido University; Kyoto University
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作者：Van Werde, Alexander; Sanders, Jaron
作者单位：Eindhoven University of Technology; University of Munster
摘要：We prove that a sum of random matrices generated by a psi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-mixing Markov chain has similar spectral properties to a Gaussian matrix with the same mean and covariance structure. This nonasymptotic universality principle enables sharp concentration i...
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作者：Otto, Felix; Palmieri, Matteo; Wagner, Christian
作者单位：Max Planck Society; Institute of Science & Technology - Austria
摘要：We study a (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 semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical 2-dimensional random field Ising model. The scaling of the correlation length of the latter was r...
