期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2018
卷号：XV
期号：2
页码：913-960
DOI：10.30757/ALEA.v15-35
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Let F(N;m) denote a random forest on a set of N vertices, chosenuniformly from all forests with m edges. Let F(N; p) denote the forest obtainedby conditioning the Erd}os-Renyi graph G(N; p) to be acyclic. We describe scalinglimits for the largest components of F(N; p) and F(N;m), in the critical windowp = N1 + O(N4=3) or m = N=2 + O(N2=3). Aldous (1997) described a scalinglimit for the largest components of G(N; p) within the critical window in terms ofthe excursion lengths of a reected Brownian motion with time-dependent drift.Our scaling limit for critical random forests is of a similar nature, but now basedon a reected di usion whose drift depends on space as well as on time.
关键词：Random forest; random graph; critical window; exploration process;
