Solution of the Kolmogorov equation for TASEP

Mihai Nica; Jeremy Quastel; Daniel Remenik

doi:10.1214/20-AOP1425

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Home > Journals > Ann. Probab. > Volume 48 > Issue 5 > Article

September 2020 Solution of the Kolmogorov equation for TASEP

Mihai Nica, Jeremy Quastel, Daniel Remenik

Ann. Probab. 48(5): 2344-2358 (September 2020). DOI: 10.1214/20-AOP1425

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Abstract

We provide a direct and elementary proof that the formula obtained in (Matetski, Quastel and Remenik (2016)) for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP particle system.

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Mihai Nica. Jeremy Quastel. Daniel Remenik. "Solution of the Kolmogorov equation for TASEP." Ann. Probab. 48 (5) 2344 - 2358, September 2020. https://doi.org/10.1214/20-AOP1425

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Received: 1 June 2019; Revised: 1 January 2020; Published: September 2020

First available in Project Euclid: 23 September 2020

MathSciNet: MR4152645

Digital Object Identifier: 10.1214/20-AOP1425

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Primary: 60K35 , 82B23 , 82C22

Keywords: KPZ fixed point , KPZ universality class , PushASEP , TASEP

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Ann. Probab.

Vol.48 • No. 5 • September 2020

Institute of Mathematical Statistics

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Mihai Nica, Jeremy Quastel, Daniel Remenik "Solution of the Kolmogorov equation for TASEP," The Annals of Probability, Ann. Probab. 48(5), 2344-2358, (September 2020)

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