Temperley-Lieb Stochastic Processes

TL;DR

This paper explores one-dimensional stochastic processes linked to the Temperley-Lieb algebra, connecting their stationary state distributions to combinatorial objects called alternating sign matrices, with implications for statistical physics and combinatorics.

Contribution

It introduces a conjecture relating stationary distributions of these processes to the enumeration of symmetry classes of alternating sign matrices.

Findings

Conjecture connecting stationary states to alternating sign matrices

Identification of boundary condition effects on process behavior

Potential new links between statistical physics and combinatorics

Abstract

We discuss one-dimensional stochastic processes defined through the Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the stationary state, to the enumeration of a symmetry class of alternating sign matrices, objects that have received much attention in combinatorics.