LGV proof of a determinantal theorem for TASEP probabilities

TL;DR

This paper provides a new bijective proof of a determinantal formula for TASEP steady state probabilities, connecting combinatorial tableaux with classical linear algebra techniques.

Contribution

It introduces a bijective proof using the Lindström-Gessel-Viennot Lemma, offering a clearer understanding of the determinantal structure in TASEP probabilities.

Findings

New bijective proof of the determinantal formula

Connection between Catalan tableaux and linear algebra

Enhanced understanding of TASEP steady state probabilities

Abstract

The Totally Asymmetric Simple Exclusion Process (TASEP) is a non-equilibrium particle model on a finite one-dimensional lattice with open boundaries. In our earlier paper, we obtained a determinantal formula that computes the steady state probabilities of this process by the enumeration of "Catalan alternative tableaux", which are certain fillings of Young diagrams. Here, we present a new, more illuminating bijective proof of this determinantal formula using the Lindstr\"{o}m-Gessel-Viennot Lemma.