Quastel, Jeremy and Rahman, Mustazee (2020) 'TASEP fluctuations with soft-shock initial data.', Annales Henri Lebesgue., 3 . pp. 999-1021.
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.
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|Publisher Web site:||https://doi.org/10.5802/ahl.52|
|Publisher statement:||This article was published under a Creative Commons license CC BY 4.0.|
|Date accepted:||14 October 2019|
|Date deposited:||04 November 2019|
|Date of first online publication:||24 August 2020|
|Date first made open access:||03 November 2020|
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