Probability Theory and Related Fields

最新文章

• Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules AI翻译
  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...
• Eve, Adam and the preferential attachment tree AI翻译
  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(...
• Symmetric cooperative motion in one dimension AI翻译
  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...
• Effective diffusivities in periodic KPZ AI翻译
  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...
• Tractability from overparametrization: the example of the negative perceptron AI翻译
  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...
• New results for the random nearest neighbor tree AI翻译
  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...
• Stationary measures for stochastic differential equations with degenerate damping AI翻译
  作者：Bedrossian, Jacob; Liss, Kyle
  作者单位：University of California System; University of California Los Angeles; Duke University
  摘要：A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic differential equations in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\...
• Functional limit theorems for Hawkes processes AI翻译
  作者：Horst, Ulrich; Xu, Wei
  作者单位：Humboldt University of Berlin; Humboldt University of Berlin; Beijing Institute of Technology
  摘要：We prove that the long-run behavior of Hawkes processes is fully determined by the average number and the dispersion of child events. For subcritical processes we provide FLLNs and FCLTs under minimal conditions on the kernel of the process with the precise form of the limit theorems depending strongly on the dispersion of child events. For a critical Hawkes process with weakly dispersed child events, functional central limit theorems do not hold. Instead, we prove that the rescaled intensity ...
• Infinite disorder renormalization fixed point for the continuum random field Ising chain AI翻译
  作者：Collin, Orphee; Giacomin, Giambattista; Hu, Yueyun
  作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
  摘要：We consider the continuum version of the random field Ising model in one dimension: this model arises naturally as weak disorder scaling limit of the original Ising model. Like for the Ising model, a spin configuration is conveniently described as a sequence of spin domains with alternating signs (domain-wall structure). We show that for fixed centered external field and as spin-spin couplings become large, the domain-wall structure scales to a disorder dependent limit that coincides with the ...
• The intransitive dice kernel: 1x ≥ y-1x ≤y/4-3(x-y) (1+xy)/8 AI翻译
  作者：Sah, Ashwin; Sawhney, Mehtaab
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：Answering a pair of questions of Conrey, Gabbard, Grant, Liu, and Morrison, we prove that a triplet of dice drawn from the multiset modelare intransitive with probability 1/4+o(1)and the probability a random pair of dice tie tends toward alpha n(-1) for an explicitly defined constant alpha. This extends and sharpens the recent results of Polymath regarding the balanced sequence model. We further show the distribution of larger tournaments converges to a universal tournamenton in both models. T...