Meteor process on

• 成果类型: Article
• 署名作者: Burdzy, Krzysztof
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0602-8
• 发表日期: 2015
• 页码: 667-711
• 关键词: brownian motions; particle; systems; FLOWS

摘要

The meteor process is a model for mass redistribution on a graph. The case of finite graphs was analyzed in Billey et al. (On meteors, earthworms and WIMPs. Ann Appl Probab, 2014). This paper is devoted to the meteor process on . The process is constructed and a stationary distribution is found. Convergence to this stationary distribution is proved for a large family of initial distributions. The first two moments of the mass distribution at a vertex are computed for the stationary distribution. For the one-dimensional lattice , the net flow of mass between adjacent vertices is shown to have bounded variance as time goes to infinity. An alternative representation of the process on as a collection of non-crossing paths is presented. The distributions of a tracer particle in this system of non-crossing paths are shown to be tight as time goes to infinity.