Partition Function Zeros of Paths and Normalization Zeros of ASEPS

TL;DR

This paper explores the connection between the zeros of the partition function in an adsorbing Dyck walk model and the ASEP normalization zeros, using conformal mapping and electrostatic analogy to analyze their thermodynamic limits.

Contribution

It introduces a novel approach linking partition function zeros of Dyck walks with ASEP normalization zeros via conformal maps and electrostatic analogies.

Findings

Derived the thermodynamic limit of ASEP normalization zeros

Established equivalence between electrostatic and conformal map approaches

Applied methods to both ASEP and random allocation models

Abstract

We exploit the equivalence between the partition function of an adsorbing Dyck walk model and the Asymmetric Simple Exclusion Process (ASEP) normalization to obtain the thermodynamic limit of the locus of the ASEP normalization zeros from a conformal map. We discuss the equivalence between this approach and using an electrostatic analogy to determine the locus, both in the case of the ASEP and the random allocation model.