Spatial random permutations with small cycle weights

• 成果类型: Article
• 署名作者: Betz, Volker; Ueltschi, Daniel
• 署名单位: University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0248-0
• 发表日期: 2011
• 页码: 191-222
• 关键词: bose-gas; percolation transition

摘要

We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certain critical density.