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作者：Gu, Chenlin; Su, Zhonggen; Xu, Ruizhe
作者单位：Tsinghua University; Zhejiang University
摘要：For the supercritical Bernoulli bond percolation on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}<^>d$$\end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl...
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作者：Benard, Timothee; Breuillard, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); University of Oxford
摘要：We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group G, where the variables are allowed to be non-centered. Our result also improves on the known centered case by proving uniformity for two-sided moderate deviations and allowing measures with a moment of order 2(dimG)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us...
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作者：Haslegrave, John; Keevash, Peter
作者单位：Lancaster University; University of Oxford
摘要：We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet. We study the equilibrium time of the process, by which we mean the number of steps taken until no further interactions can occur. Under a rather general framework, we obtain high probability upper and lower bounds on the equilibrium time that match up to a c...
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作者：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions d > 6. We obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. In a companion paper, we apply a similar analysis to the study of the weakly self-avoiding walk model in dimensions d > 4 [Duminil-Copin and Panis, arXiv:2410.03649, (2024)].
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作者：Kim, Yujin H.; Zeitouni, Ofer
作者单位：New York University; Weizmann Institute of Science; New York University
摘要：We study the shape of the outer envelope of a branching Brownian motion (BBM) in Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>d$$\end{document}, d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Ji, Hong Chang
作者单位：Institute of Science & Technology - Austria; University of Arizona; University of Wisconsin System; University of Wisconsin Madison
摘要：For general large non-Hermitian random matrices X and deterministic normal deformations A, we prove that the local eigenvalue statistics of A+X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A+X$$\end{document} close to the critical edge points of its spectrum are universal. This concludes the proof of the third an...
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作者：Du, Hang; Gong, Shuyang; Huang, Rundong
作者单位：Massachusetts Institute of Technology (MIT); Peking University
摘要：We study the graph alignment problem over two independent Erdos-R & eacute;nyi random graphs on n vertices, with edge density p falling into two regimes separated by the critical window around p(c ):= root log n/n. Our result reveals an algorithmic phase transition for this random optimization problem: polynomial-time approximation schemes exist in the sparse regime, while statistical-computational gap emerges in the dense regime. Additionally, we establish a sharp transition on the performanc...
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作者：Hazra, Rajat Subhra; den Hollander, Frank; Parvaneh, Azadeh
作者单位：Leiden University; Leiden University - Excl LUMC
摘要：Let Gn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_n$$\end{document} be an undirected finite graph on n is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...
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作者：Li, Xinyi; Shiraishi, Daisuke
作者单位：Peking University; Kyoto University
摘要：In this work we consider loop-erased random walk (LERW) and its scaling limit in three dimensions, and prove that 3D LERW parametrized by renormalized length converges to its scaling limit parametrized by some suitable measure with respect to the uniform convergence topology in the lattice size scaling limit. Our result greatly improves the work (Kozma in Acta Math 199:29-152, 2007) of Gady Kozma which establishes the weak convergence of the rescaled trace of 3D LERW towards a random compact s...
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作者：Barnes, Clayton; Mytnik, Leonid; Sun, Zhenyao
作者单位：Technion Israel Institute of Technology; Beijing Institute of Technology
摘要：Consider the [0, 1]-valued continuous random field solution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u_t(x))_{t\ge 0, x\in {\mathbb {R}}}$$\end{document} to the one-dimensional stochastic heat equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{...
