Markov processes related to the stationary measure for the open KPZ equation

• 成果类型: Article
• 署名作者: Bryc, Wlodek; Kuznetsov, Alexey; Wang, Yizao; Wesolowski, Jacek
• 署名单位: University System of Ohio; University of Cincinnati; York University - Canada; Warsaw University of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01110-7
• 发表日期: 2023
• 页码: 353-389
• 关键词: Polynomials; Transforms; asep

摘要

We provide a probabilistic description of the stationary measures for the open KPZ on the spatial interval [0, 1] in terms of a Markov process Y, which is a Doob's h transform of the Brownian motion killed at an exponential rate. Our work builds on a recent formula of Corwin and Knizel which expresses the multipoint Laplace transform of the stationary solution of the open KPZ in terms of another Markov process T: the continuous dual Hahn process with Laplace variables taking on the role of time-points in the process. The core of our approach is to prove that the Laplace transforms of the finite dimensional distributions of Y and T are equal when the time parameters of one process become the Laplace variables of the other process and vice versa.