Limit behavior of the Bak-Sneppen evolution model
成果类型：
Article
署名作者：
Meester, R; Znamenski, D
署名单位：
Vrije Universiteit Amsterdam
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2003
页码：
1986-2002
关键词：
摘要：
One of the key problems related to the Bak-Sneppen evolution model on the circle is computing the limit distribution of the fitness at a fixed observation vertex in the stationary regime as the size of the system tends to infinity. Some simulations have suggested that this limit distribution is uniform on (f, 1) for some f similar to 2/3. In this article, we prove that the mean of the fitness in the stationary regime is bounded away from 1, uniformly in the size of the system, thereby establishing the nontriviality of the limit behavior. The Bak-Sneppen dynamics can easily be defined on any finite connected graph. We also present a generalization of the phase-transition result in the context of an increasing sequence of such graphs. This generalization covers the multidimentional Bak-Sneppen model as well as the Bak-Sneppen model on a tree. Our proofs are based on a self-similar graphical representation of the avalanches.