Local Neighbourhoods for First-Passage Percolation on the Configuration Model

被引：0
作者：
Steffen Dereich
Marcel Ortgiese
机构：
[1] Westfälische Wilhelms-Universität Münster,Institut für Mathematische Statistik
[2] University of Bath,Department of Mathematical Sciences
来源：
Journal of Statistical Physics | 2018年 / 173卷
关键词：
First passage percolation; Random graphs; Configuration model; Local limit; Geodesics; Branching processes; Primary 05C80; Secondary 60J80;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider first-passage percolation on the configuration model. Once the network has been generated each edge is assigned an i.i.d. weight modeling the passage time of a message along this edge. Then independently two vertices are chosen uniformly at random, a sender and a recipient, and all edges along the geodesic connecting the two vertices are coloured in red (in the case that both vertices are in the same component). In this article we prove local limit theorems for the coloured graph around the recipient in the spirit of Benjamini and Schramm. We consider the explosive regime, in which case the random distances are of finite order, and the Malthusian regime, in which case the random distances are of logarithmic order.
引用
收藏
页码：485 / 501
页数：16
相关论文
共 31 条
  • [1] Amini O(2013)On explosions in heavy-tailed branching random walks Ann. Probab. 41 1864-1899
  • [2] Devroye L(2017)Nonuniversality of weighted random graphs with infinite variance degree J. Appl. Probab. 54 146-164
  • [3] Griffiths S(2001)Recurrence of distributional limits of finite planar graphs Electron. J. Probab. 6 13-1826
  • [4] Olver N(2008)First passage percolation on locally treelike networks. I. Dense random graphs J. Math. Phys. 49 125218-738
  • [5] Baroni E(2015)Degree distribution of shortest path trees and bias of network sampling algorithms Ann. Appl. Probab. 25 1780-707
  • [6] van der Hofstad R(2010)Extreme value theory, Poisson–Dirichlet distributions, and first passage percolation on random networks Adv. Appl. Probab. 42 706-1965
  • [7] Komjáthy J(2011)First passage percolation on the Erdős–Rényi random graph Comb. Probab. Comput. 20 683-2630
  • [8] Benjamini I(2010)First passage percolation on random graphs with finite mean degrees Ann. Appl. Probab. 20 1907-237
  • [9] Schramm O(2017)Universality for first passage percolation on sparse random graphs Ann. Probab. 45 2568-259
  • [10] Bhamidi S(2001)First-passage percolation on the random graph Probab. Eng. Inf. Sci. 15 225-undefined
1234