Interacting particle systems and random walks on Hecke algebras

Abstract

In this paper we show that a variety of interacting particle systems with multiple species can be viewed as random walks on Hecke algebras. This class of systems includes the asymmetric simple exclusion process (ASEP), M-exclusion TASEP, ASEP(q,j), stochastic vertex models, and many others. As an application, we study the asymptotic behavior of second class particles in some of these systems.

References in corpus (4)

• The TASEP speed process
• The oriented swap process
• The shape of a random affine Weyl group element and random core partitions
• Stochastic Fusion of Interacting Particle Systems and Duality Functions

Cited by in corpus (6)

• A central limit theorem for descents of a Mallows permutation and its inverse
• Observables of stochastic colored vertex models and local relation
• Mallows Product Measure
• Two dualities: Markov and Schur-Weyl
• TASEP with a general initial condition and a deterministically moving wall
• Shift-Invariance of the Colored TASEP and Finishing Times of the Oriented Swap Process