TASEP fluctuations with soft-shock initial data

Quastel, Jeremy; Rahman, Mustazee

doi:10.5802/ahl.52

TASEP fluctuations with soft-shock initial data

Quastel, Jeremy; Rahman, Mustazee

Authors

Jeremy Quastel

Dr Mustazee Rahman mustazee.rahman@durham.ac.uk
Associate Professor

Abstract

We consider the totally asymmetric simple exclusion process with soft-shock initial particle density, which is a step function increasing in the direction of flow and the step size chosen small to admit KPZ scaling. The initial configuration is deterministic and the dynamics create a shock. We prove that the fluctuations of a particle at the macroscopic position of the shock converge to the maximum of two independent GOE Tracy-Widom random variables, which establishes a conjecture of Ferrari and Nejjar. Furthermore, we show the joint fluctuations of particles near the shock are determined by the maximum of two lines described in terms of these two random variables. The microscopic position of the shock is then seen to be their difference. Our proofs rely on determinantal formulae and a novel factorization of the associated kernels.

Citation

Quastel, J., & Rahman, M. (2020). TASEP fluctuations with soft-shock initial data. Annales Henri Lebesgue, 3, 999-1021. https://doi.org/10.5802/ahl.52

Journal Article Type	Article
Acceptance Date	Oct 14, 2019
Online Publication Date	Aug 24, 2020
Publication Date	2020-08
Deposit Date	Nov 4, 2019
Publicly Available Date	Nov 3, 2020
Journal	Annales Henri Lebesgue
Publisher	École Normale Supérieure de Rennes
Peer Reviewed	Peer Reviewed
Volume	3
Pages	999-1021
DOI	https://doi.org/10.5802/ahl.52
Related Public URLs	https://arxiv.org/abs/1801.06143