Size of the largest cluster under zero-range invariant measures

• 成果类型: Article
• 署名作者: Jeon, I; March, P; Pittel, B
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 1162-1194
• 关键词: polymerization; partitions; MODEL; EQUATIONS; gelation; graph; limit; gel

摘要

We study the finite zero-range process with occupancy-dependent rate function g(.). Under the invariant measure, which can be written explicitly in terms of g, particles are distributed over sites and we regard all particles at a fixed site as a cluster. In the density one case, that; is, equal numbers of particles and sites, we determine asymptotically the size of the largest cluster, as the number of particles tends to infinity, and determine? its dependence on the rate function.