The half-space Airy stat process

Abstract

We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-Péché, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors.

51 pages, 3 figures, added Appendix D

References in corpus (9)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Fluctuation properties of the TASEP with periodic initial configuration
• The one-dimensional KPZ equation and its universality class
• Fluctuations of the one-dimensional polynuclear growth model with external sources
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• From interacting particle systems to random matrices
• A phase transition for $q$-TASEP with a few slower particles
• Memory and universality in interface growth
• Statistics of TASEP with three merging characteristics