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arXiv · 2601.21412

Leaders in multi-type TASEP

Alexei Borodin·Alexey Bufetov
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Abstract

We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with step initial condition, in which all particles have distinct types. Our main object of interest is the type of the rightmost particle -- the leader -- at large time $t$. We prove a central limit theorem for this random variable. Somewhat unexpectedly, the problem is closely connected to certain observables of voter and coalescing processes on $\mathbb{Z}$; we therefore derive their asymptotics as well. We also analyze the large-time behavior of a few other related observables, including certain multi-particle ones.

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Alexei Borodin, Alexey Bufetov. 2026-01-29. Leaders in multi-type TASEP. https://arxiv.org/abs/2601.21412

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