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
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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
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. 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
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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
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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:
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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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