TASEP and generalizations: method for exact solution

• 成果类型: Article
• 署名作者: Matetski, Konstantin; Remenik, Daniel
• 署名单位: Columbia University; Universidad de Chile; Universidad de Chile
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01129-w
• 发表日期: 2023
• 页码: 615-698
• 关键词: large time asymptotics; polynuclear growth; fluctuations; ensembles; DYNAMICS; equation; tilings; models; chain; png

摘要

The explicit biorthogonalization method, developed in [24] for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evolution of several interacting particle systems in the KPZ universality class. The method is applied to sequential and parallel update versions of each of the four variants of discrete time TASEP (with Bernoulli and geometric jumps, and with block and push dynamics) which have determinantal transition probabilities; to continuous time PushASEP; and to a version of TASEP with generalized update. In all cases, multipoint distribution functions are expressed in terms of a Fredholm determinant with an explicit kernel involving hitting times of certain random walks to a curve defined by the initial data of the system. The method is further applied to systems of interacting caterpillars, an extension of the discrete time TASEP models which generalizes sequential and parallel updates.