Asymptotics of dynamic ASEP using duality

TL;DR

This paper investigates the asymptotic behavior of dynamic ASEP, showing it converges to Tracy--Widom distribution or remains bounded, and extends duality methods to multi-species ASEP with contour integral formulas.

Contribution

It introduces a new asymptotic analysis method for dynamic ASEP using orthogonal polynomial duality and generalizes duality techniques to multi-species ASEP.

Findings

Dynamic ASEP asymptotics follow Tracy--Widom distribution or are bounded.

Contour integral formulas for multi-species ASEP are derived.

The method advances understanding of ASEP asymptotics and duality applications.

Abstract

Using a recently developed method for proving asymptotics via orthogonal polynomial duality arXiv:2305.17602, we prove that the dynamic ASEP introduced in arXiv:1701.05239 has asymptotics which are either distributed as the Tracy--Widom \(F_2,\) or are almost surely bounded. Using a different duality, we also provide contour integrals formulas for multi--species ASEP, which generalize results for the single--species ASEP.