ASEP via Mallows coloring
Alexei Borodin, Alexey Bufetov

TL;DR
This paper investigates the asymptotic behavior of ASEP with finitely many particles under a specific randomized initial condition, revealing its KPZ limit behavior and introducing a novel Mallows permutation coloring technique.
Contribution
It introduces a new coloring method for ASEP particles using Mallows permutations and analyzes the process's KPZ limit behavior under certain initial conditions.
Findings
ASEP with finitely many particles exhibits KPZ limit behavior.
A new Mallows permutation-based coloring technique for ASEP particles.
The randomized initial condition is optimal for asymptotic analysis.
Abstract
In this paper we study the asymptotic behavior of the Asymmetric Simple Exclusion Process (=ASEP) with finitely many particles. It turns out that a certain randomized initial condition is the most amenable to such an analysis. Our main result is the behavior of such an ASEP in the KPZ limit regime. A key technical tool introduced in the paper -- the coloring of ASEP particles with the use of random Mallows permutations -- may be of independent interest.
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Taxonomy
TopicsDNA and Biological Computing · Machine Learning and Data Classification
