Mapping TASEP back in time

• 成果类型: Article
• 署名作者: Petrov, Leonid; Saenz, Axel
• 署名单位: Kharkevich Institute for Information Transmission Problems of the RAS; University of Virginia; University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01074-0
• 发表日期: 2022
• 页码: 481-530
• 关键词: gelfand-tsetlin graph; infinite-dimensional diffusions; random-walks; particle process; growth-models; DYNAMICS; limit; probability; asymptotics; BOUNDARY

摘要

We obtain a new relation between the distributions mu(t) at different times t >= 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions mu(t) backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving mu(t) which in turn brings new identities for expectations with respect to mu(t). The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang-Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.