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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 - Excl LUMC; Leiden University
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：Hermon, Jonathan; Huang, Xiangying; Pedrotti, Francesco; Salez, Justin
作者单位：University of British Columbia; University of North Carolina; University of North Carolina Chapel Hill; Swiss Federal Institutes of Technology Domain; ETH Zurich; Universite PSL; Universite Paris-Dauphine
摘要：Motivated by the Asymptotic Equipartition Property and its recently discovered role in the cutoff phenomenon, we initiate the systematic study of varentropy on discrete groups. Our main result is an approximate tensorization inequality which asserts that the varentropy of any conjugacy-invariant random walk is, up to a universal multiplicative constant, at most that of the free Abelian random walk with the same jump rates. In particular, it is always bounded by the number d of generators, unif...
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作者：Galeati, Lucio; Grotto, Francesco; Maurelli, Mario
作者单位：University of L'Aquila; University of Pisa
摘要：We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and Holder regular in space (rough Kraichnan's model), a well-established synthetic model of passive scalar turbulence. By studying the evolution of negative Sobolev norms, we show an anomalous regularization effect induced by the dynamics: distributional initial conditions immediately become functions of positive Sobolev regularity.
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作者：Faggionato, Alessandra
作者单位：Sapienza University Rome
摘要：Mott's variable range hopping (v.r.h.) is the phonon-induced hopping of electrons in disordered solids (such as doped semiconductors) within the regime of strong Anderson localization. It was introduced by N. Mott to explain the anomalous low temperature conductivity decay in dimension d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{...
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作者：Bao, Zhigang; George, Daniel Munoz
作者单位：University of Hong Kong
摘要：From the study of the high order freeness of random matrices, it is known that the order r cumulant of the trace of a polynomial of N-dimensional GUE/GOE is of order N2-r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N<<^>>{2-r}$$\end{document} if r is fixed. In this work, we extend the study along three direction...
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作者：Su, Yiming; Zhang, Deng
作者单位：Hangzhou Normal University; Shanghai Jiao Tong University
摘要：We study the bubbling phenomena for focusing mass-critical nonlinear Schr & ouml;dinger equations, driven by linear multiplicative noise in the sense of controlled rough paths. In both dimensions one and two, we give a pathwise construction of stochastic multi-bubble blow-up solutions, which concentrate at finitely many distinct points, and behave asymptotically like a sum of pseudo-conformal blow-up solutions. In particular, this provides the first examples of mass quantization phenomenon in ...
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作者：Cai, Zhenhao; Procaccia, Eviatar B.; Zhang, Yuan
作者单位：Weizmann Institute of Science; Technion Israel Institute of Technology; Renmin University of China; Renmin University of China
摘要：We study the harmonic measure (i.e. the limit of the hitting distribution of a simple random walk starting from a distant point) on three canonical two-dimensional lattices: the square lattice Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}<^>2$$\end{document}, the triangular lattice T\documentclass[1...
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作者：Fredes, Luis; Sepulveda, Avelio
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：The (non-spanning) tree decorated quadrangulation is a random pair consisting of a quadrangulation and a subtree chosen uniformly over the set of pairs with a prescribed size. In this paper, we study the tree decorated quadrangulation in the critical regime: when the number f of faces of the map is proportional to the square of the size of the tree. We show that with high probability in this regime, the diameter of the tree lies between o(f(1/4)) and f(1/4)/log(alpha)(f), for all alpha > 1. Th...
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作者：Bolbotowski, Karol; Bouchitte, Guy
作者单位：University of Warsaw
摘要：Based on a new Kantorovich-Rubinstein duality principle for the Hessian that was recently established by the two authors, we extend the Rio inequality to any dimension d >= 1 with an optimal constant. Similarly, we propose an optimal upper bound for the ratio of Zolotarev distance Z2(mu,nu) to Wasserstein distance W2(mu,nu) when mu,nu is an element of P2(Rd) are centred probabilities with prescribed variances.
