A martingale problem for an absorbed diffusion: the nucleation phase of condensing zero range processes

• 成果类型: Article
• 署名作者: Beltran, J.; Jara, M.; Landim, C.
• 署名单位: Pontificia Universidad Catolica del Peru; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0749-6
• 发表日期: 2017
• 页码: 1169-1220
• 关键词: invariant-measures; condensation; DYNAMICS; limit

摘要

We prove uniqueness of a martingale problem with boundary conditions on a simplex associated to a differential operator with an unbounded drift. We show that the solution of the martingale problem remains absorbed at the boundary once it attains it, and that, after hitting the boundary, it performs a diffusion on a lower dimensional simplex, similar to the original one. We also prove that in the diffusive time scale condensing zero-range processes evolve as this absorbed diffusion.