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作者：Alvarado, Jose D.; de Oliveira, Leonardo Goncalves; Griffiths, Simon
作者单位：University of Ljubljana
摘要：We consider the question of determining the probability of triangle count deviations in the Erdos-Renyi random graphs G (n,m) and G (n,p)with densities larger than n(-1/2)(log n)(1/2). In particular, we determine the log probability log P(N-Delta(G) > (1+delta)p(3)n(3))up to a constant factor across essentially the entire range of possible deviations, in both the G (n,m) and G (n,p) model. For the G(n,p) model, we also prove a stronger result, up to a(1+o(1)) factor, in the non-localised regim...
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作者：Favaro, S.; Hanin, B.; Marinucci, D.; Nourdin, I.; Peccati, G.
作者单位：University of Turin; Princeton University; University of Rome Tor Vergata; University of Luxembourg
摘要：We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant n. Under mild assumptions on the non-linearity, we obtain quantitative bounds on normal approximations valid at large but finite n and any fixed network depth. Our theorems show both for the finite-dimensional distributions and the entire process, that the distance between a random fully connected network (and its derivative...
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作者：Mukherjee, Chiranjib; Recke, Konstantin
作者单位：University of Munster
摘要：Let G be the Cayley graph of a finitely generated, infinite group Gamma . We show that Gamma has the Haagerup property if and only if for every alpha<1 , there is a Gamma -invariant bond percolation P on G with E[deg(omega)(g)]>alpha degG(g) for every vertex g and with the two-point function tau(g,h)=P[g <-> h] vanishing as d(g,h)->infinity . As an upshot, we also obtain a sufficient condition for the Haagerup property using Bernoulli percolation and the associated threshold pconn of random co...
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作者：Hartung, Lisa; Louidor, Oren; Wu, Tianqi
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：In this work, we resolve three open questions which were raised recently concerning the limiting extremal and cluster point processes of branching Brownian Motion. The former process records the heights of all extreme values of the motion, while the latter records the relative heights of extreme values in a genealogical neighborhood of order unity around a local maximum thereof. For the extremal point process, we show that first order asymptotics for its mass away from zero holds almost-surely...
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作者：Jorritsma, Joost; Komjathy, Julia; Mitsche, Dieter
作者单位：University of Oxford; Delft University of Technology; Pontificia Universidad Catolica de Chile
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作者：Ganguly, Ankan; Spiliopoulos, Konstantinos; Sussman, Daniel
作者单位：Boston University
摘要：We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include n agents, whose opinions are given by latent stochastic processes, and a dynamic network process describing agent interactions. Models in this class incorporate (a) bi-directional feedback between the latent processes and the network process, (b) persistence effects, meaning that the network structure at the current time depe...
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作者：Can, Van Hao; Kubota, Naoki; Nakajima, Shuta
作者单位：Vietnam Academy of Science & Technology (VAST); Nihon University; Keio University
摘要：In this paper, we study the upper tail large deviation for the one-dimensional frog model. In this model, sleeping and active frogs are assigned to sites of Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}$$\end{document}. While sleeping frogs do not move, the active ones move as independent simple rand...
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作者：Divol, Vincent; Guerin, Helene; Nguyen, Dinh-Toan; Tran, Viet Chi
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSAE Paris; University of Quebec; University of Quebec Montreal; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Montreal
摘要：From the observation of a diffusion path (Xt)t is an element of[0,T]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X_t)_{t\in [0,T]}$$\end{document} on a compact connected d-dimensional manifold M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \us...
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Bonn; Imperial College London; University of Cambridge
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作者：Qin, Shuo
摘要：Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions d=1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=1,2$$\end{document}, and that it is transient for all reinforcement parameters in ...
