Skip to main content

Research Repository

Advanced Search

TASEP fluctuations with soft-shock initial data

Quastel, Jeremy; Rahman, Mustazee

TASEP fluctuations with soft-shock initial data Thumbnail


Jeremy Quastel


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.


Quastel, J., & Rahman, M. (2020). TASEP fluctuations with soft-shock initial data. Annales Henri Lebesgue, 3, 999-1021.

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
Related Public URLs


You might also like

Downloadable Citations