Free energy distribution of the stationary O'Connell-Yor directed random polymer model

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.

39 pages, 3 figures

References in corpus (4)

• Growing interfaces uncover universal fluctuations behind scale invariance
• KPZ equation limit of higher-spin exclusion processes
• Memory and universality in interface growth
• Determinantal structures in the O'Connell-Yor directed random polymer model

Cited by in corpus (4)

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• Stationary half-space last passage percolation
• Upper tail bounds for stationary KPZ models
• Borodin-Péché fluctuations of the free energy in directed random polymer models