LARGE DEVIATIONS FOR THE EXCLUSION PROCESS WITH A SLOW BOND

• 成果类型: Article
• 署名作者: Franco, Tertuliano; Neumann, Adriana
• 署名单位: Universidade Federal da Bahia; Universidade Federal do Rio Grande do Sul
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1287
• 发表日期: 2017
• 页码: 3547-3587
• 关键词: phase-transition; BEHAVIOR

摘要

We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the slow bond, has associated transition rate of value N-1, where N is the scaling parameter. This model has been considered in previous works on the subject of hydrodynamic limit and fluctuations. In this paper, assuming uniqueness for weak solutions of hydrodynamic equation associated to the perturbed process, we obtain dynamical large deviations estimates in the diffusive scaling. The main challenge here is the fact that the presence of the slow bond gives rise to Robin's boundary conditions in the continuum, substantially complicating the large deviations scenario.