2017/01/31 by Takashi Imamura, Tomohiro Sasamoto · 13 citations
Mathematics · Physics and Astronomy · #Distribution (mathematics) #Energy (signal processing) #Fredholm determinant #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Polymer #Random Matrices and Applications #Stationary distribution #Stationary state #Stochastic processes and statistical mechanics #Work (physics) #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.1088/1751-8121/aa6e17
published in Journal of Physics A Mathematical and Theoretical 50(28), 285203 (Institute of Physics) · 39 pages, 3 figures
openalex created_date 2017/02/03 · arxiv created 2017/02/04 · openalex publication_date 2017/04/20 · arxiv updated 2017/08/02 · openalex updated_date 2026/08/05
Abstract We study the semi-discrete directed polymer model introduced by O’Connell–Yor in its stationary regime, based on our previous work on the stationary q -totally asymmetric simple exclusion process ( q -TASEP) using a two-sided q -Whittaker process. We give a formula for the free energy distribution of the polymer model in terms of Fredholm determinant and show that the universal KPZ stationary distribution appears in the long time limit. We also consider the limit to the stationary KPZ equation and discuss the connections with previously found formulas.