Fluctuations of the competition interface in presence of shocks

TL;DR

This paper investigates the behavior of the competition interface in last passage percolation models with shocks, analyzing its fluctuations and distribution around the shock, extending previous results to more complex scenarios.

Contribution

It extends the analysis of competition interface fluctuations from rarefaction fans to shock scenarios in LPP models, providing new distributional results.

Findings

Law of fluctuations around the deterministic position derived

Multipoint distribution around the shock characterized

Results extend previous one-point fluctuation analysis

Abstract

We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied by Ferrari and Pimentel in [Ann. Probab. 33 (2005), 1235-1254] for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deterministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of [Probab. Theory Relat. Fields 61 (2015), 61-109].