Stationary half-space last passage percolation

Abstract

In this paper we study stationary last passage percolation (LPP) in half-space geometry. We determine the limiting distribution of the last passage time in a critical window close to the origin. The result is a new two-parameter family of distributions: one parameter for the strength of the diagonal bounding the half-space (strength of the source at the origin in the equivalent TASEP language) and the other for the distance of the point of observation from the origin. It should be compared with the one-parameter family giving the Baik--Rains distributions for full-space geometry. We finally show that far enough away from the characteristic line, our distributions indeed converge to the Baik--Rains family. We derive our results using a related integrable model having Pfaffian structure together with careful analytic continuation and steepest descent analysis.

arXiv comment41 pages, 4 figures

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Cited by in corpus (8)

• Half-space stationary Kardar-Parisi-Zhang equation
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• Lyapunov exponents of the half-line SHE
• Half-space stationary Kardar-Parisi-Zhang equation beyond the Brownian case
• Mixing times and cutoff for the TASEP in the high and low density phase
• Discrete and continuous Muttalib--Borodin processes I: the hard edge
• The half-space Airy stat process
• The second class particle in the half-line open TASEP