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arXiv · 2204.05395

The ASEP speed process

Amol Aggarwal·Ivan Corwin·Promit Ghosal
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Abstract

For ASEP with step initial data and a second class particle started at the origin we prove that as time goes to infinity the second class particle almost surely achieves a velocity that is uniformly distributed on $[-1,1]$. This positively resolves Conjecture 1.9 and 1.10 of [Amir, Angel and Valko, "The TASEP speed process", Annals of Probability 39, 1205--1242, 2011] and allows us to construct the ASEP speed process.

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Amol Aggarwal, Ivan Corwin, Promit Ghosal. 2022-04-11. The ASEP speed process. https://arxiv.org/abs/2204.05395

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