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作者：Banerjee, Sayan; Bhamidi, Shankar; Huang, Xiangying
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Co-evolving network models, wherein dynamics such as randomwalks on the network influence the evolution of the network structure, which in turn influences the dynamics, are of interest in a range of domains. While much of the literature in this area is currently supported by numerics, providing evidence for fascinating conjectures and phase transitions, proving rigorous results has been quite challenging. We propose a general class of co-evolving tree network models driven by local exploration...
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作者：Gass, Louis; Stecconi, Michele
作者单位：University of Luxembourg
摘要：Let f be a Gaussian random field on 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} and let X be the number of critical points of f contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on f, the random variable X has...
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作者：Suzuki, Kohei
作者单位：Durham University
摘要：In this paper, we provide relations among the following properties: (a) the tail triviality of a probability measure mu on the configuration space Gamma; (b) the finiteness of a suitable L-2-transportation-type distance (d) over bar (Gamma); (c) the irreducibility of local mu-symmetric Dirichlet forms on Gamma. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/p...
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作者：Baran, Zsuzsanna; Hermon, Jonathan; Sarkovic, Andela; Sousi, Perla
作者单位：University of Cambridge; University of British Columbia
摘要：For a finite graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=(V,E)$$\end{document} let G & lowast;\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：Duminil-Copin, Hugo; Hartarsky, Ivailo
作者单位：University of Geneva; Universite Paris Saclay; Technische Universitat Wien
摘要：We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This extends previous instances proved for several specific rules. The paper supersedes a draft by Alexander Holroyd and the first author from 2012. While it served a role in the subsequent development of bootstrap percolation universality, we have chosen to adopt a mo...
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作者：Contat, Alice; Curien, Nicolas; Lacroix, Perrine; Lasalle, Etienne; Rivoirard, Vincent
作者单位：Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine
摘要：We consider the problem of finding the initial vertex (Adam) in a Barab & aacute;si-Albert tree process (T(n) : n >= 1) at large times. More precisely, given epsilon > 0, one wants to output a subset P (epsilon)(n) of vertices of T(n) so that the initial vertex belongs to P (epsilon)(n) with probability at least 1-epsilon when n is large. It has been shown by Bubeck, Devroye and Lugosi, refined later by Banerjee and Huang, that one needs to output at least epsilon(-1+o(1)) and at most epsilon(...
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作者：Addario-Berry, Louigi; Beckman, Erin; Lin, Jessica
作者单位：McGill University; Utah System of Higher Education; Utah State University
摘要：We explore the relationship between recursive distributional equations and convergence results for finite difference schemes of parabolic partial differential equations (PDEs). We focus on a family of random processes called symmetric cooperative motions, which generalize the symmetric simple random walk and the symmetric hipster random walk introduced in Addario-Berry et al. (Probab Theory Related fields 178(1-2):437-473, 2020). We obtain a distributional convergence result for symmetric coop...
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作者：Gu, Yu; Komorowski, Tomasz
作者单位：University System of Maryland; University of Maryland College Park; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：For the KPZ equation on a torus with 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} spacetime white noise, it was shown in Dunlap et al. (Commun Pure Appl Math, 2023, https://doi.org/10.1002/cpa.22110) and Gu and Komorowski (Ann Inst H Poincare Prob Stat, 2021, arXiv:2104.13540v2) that the...
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作者：Montanari, Andrea; Zhong, Yiqiao; Zhou, Kangjie
作者单位：Stanford University; Stanford University; University of Wisconsin System; University of Wisconsin Madison
摘要：In the negative perceptron problem we are given n data points (xi,yi)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varvec{x}_i,y_i)$$\end{document}, where xi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs...
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作者：Lichev, Lyuben; Mitsche, Dieter
作者单位：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; Bulgarian Academy of Sciences
摘要：In this paper, we study the online nearest neighbor random tree in dimension d is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\in {\mathbb {N}}$$\end{document} (called d-NN tree for short) defined as follows. We fix the torus Tnd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasy...
