SCALING LIMIT FOR BROWNIAN MOTIONS WITH ONE-SIDED COLLISIONS

• 成果类型: Article
• 署名作者: Ferrari, Patrik L.; Spohn, Herbert; Weiss, Thomas
• 署名单位: University of Bonn
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1025
• 发表日期: 2015
• 页码: 1349-1382
• 关键词: tasep; fluctuations; systems; models

摘要

We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a SchUtz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, that is, particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. In the appropriate large time scaling limit, the fluctuations in the particle positions are described by the Airy(1) process.