# Interacting particle systems and random walks on Hecke algebras

@article{Bufetov2020InteractingPS, title={Interacting particle systems and random walks on Hecke algebras}, author={Alexey Bufetov}, journal={arXiv: Probability}, year={2020} }

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.

## 11 Citations

Symmetries of stochastic colored vertex models

- MathematicsThe Annals of Probability
- 2021

Author(s): Galashin, Pavel | Abstract: We discover a new property of the stochastic colored six-vertex model called flip invariance. We use it to show that for a given collection of observables of…

Shift invariance of half space integrable models

- Mathematics
- 2022

. We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six…

Observables of Stochastic Colored Vertex Models and Local Relation

- MathematicsCommunications in Mathematical Physics
- 2021

We study the stochastic colored six vertex (SC6V) model and its fusion. Our main result is an integral expression for natural observables of this model -- joint q-moments of height functions. This…

Two Dualities: Markov and Schur–Weyl

- Mathematics
- 2020

We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases:
(1) Using a Schur-Weyl duality…

Cutoff profile of ASEP on a segment

- MathematicsProbability Theory and Related Fields
- 2022

This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N and finds that for particle densities in (0, 1), the total-variation cutoff window of ASEP is N 1 / 3 and the cutoff profile is 1-F GUE, where F GUE is the Tracy-Widom distribution function.

TASEP with a moving wall

- Mathematics
- 2021

We consider a totally asymmetric simple exclusion on Z with the step initial condition, under the additional restriction that the first particle cannot cross a deterministally moving wall. We prove…

To fixate or not to fixate in two-type annihilating branching random walks

- MathematicsThe Annals of Probability
- 2021

We study a model of competition between two types evolving as branching random walks on $\mathbb{Z}^d$. The two types are represented by red and blue balls respectively, with the rule that balls of…

Shock fluctuations in TASEP under a variety of time scalings

- Mathematics
- 2020

We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities, made by block of fully packed particles. Initially a second class…

microscopic derivation of coupled SPDE’s with a

- Mathematics
- 2022

. This paper is concerned with the relationship between forward–backward stochastic Volterra integral equations (FBSVIEs, for short) and a system of (nonlocal in time) path dependent partial…

A central limit theorem for descents of a Mallows permutation and its inverse

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2022

This paper studies the asymptotic distribution of descents $\des(w)$ in a permutation $w$, and its inverse, distributed according to the Mallows measure. The Mallows measure is a non-uniform…

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