# Dynamical stochastic higher spin vertex models

@article{Aggarwal2017DynamicalSH, title={Dynamical stochastic higher spin vertex models}, author={Amol Aggarwal}, journal={Selecta Mathematica}, year={2017}, volume={24}, pages={2659-2735} }

We introduce a new family of integrable stochastic processes, called dynamical stochastic higher spin vertex models, arising from fused representations of Felder’s elliptic quantum group $$E_{\tau , \eta } ({\mathfrak {s}}{\mathfrak {l}}_2)$$Eτ,η(sl2). These models simultaneously generalize the stochastic higher spin vertex models, studied by Corwin–Petrov and Borodin–Petrov, and are dynamical in the sense of Borodin’s recent stochastic interaction round-a-face models. We provide explicit…

## 16 Citations

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

- Mathematics
- 2020

In this paper we consider the Higher Spin Six Vertex Model on the lattice
$${\mathbb {Z}}_{\ge 2} \times {\mathbb {Z}}_{\ge 1}$$
. We first identify a family of translation invariant measures and…

Coloured stochastic vertex models and their spectral theory

- Mathematics
- 2018

This work is dedicated to $\mathfrak{sl}_{n+1}$-related integrable stochastic vertex models; we call such models coloured. We prove several results about these models, which include the following: …

Stationary Higher Spin Six Vertex Model and $q$-Whittaker measure.

- Mathematics
- 2019

In this paper we consider the Higher Spin Six Vertex Model on the lattice $\mathbb{Z}_{\geq 2} \times \mathbb{Z}_{\geq 1}$. We first identify a family of translation invariant measures and…

Nonsymmetric Macdonald polynomials via integrable vertex models

- MathematicsTransactions of the American Mathematical Society
- 2020

Starting from an integrable rank-$n$ vertex model, we construct an explicit family of partition functions indexed by compositions $\mu = (\mu_1,\dots,\mu_n)$. Using the Yang-Baxter algebra of the…

Stochastic Fusion of Interacting Particle Systems and Duality Functions

- Mathematics
- 2019

We introduce a new method, which we call stochastic fusion, which takes an exclusion process and constructs an interacting particle systems in which more than one particle may occupy a lattice site.…

HALF-SPACE MACDONALD PROCESSES

- MathematicsForum of Mathematics, Pi
- 2020

Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the…

YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS

- MathematicsForum of Mathematics, Sigma
- 2019

Employing bijectivization of summation identities, we introduce local stochastic moves based on the Yang–Baxter equation for $U_{q}(\widehat{\mathfrak{sl}_{2}})$ . Combining these moves leads to a…

Classification of Stationary distributions for the stochastic vertex models

- Mathematics
- 2022

. In this paper, we study the stationary distribution for the stochastic vertex models. Our main focus is the stochastic six vertex (S6V) model. We show that the extreme stationary distributions of…

Representation theoretic interpretation and interpolation properties of inhomogeneous spin $q$-Whittaker polynomials

- Mathematics
- 2022

. We establish new properties of inhomogeneous spin q -Whittaker polynomials, which are symmetric polynomials generalizing t = 0 Macdonald polynomials. We show that these polynomials are deﬁned in…

KPZ Equation Limit of Stochastic Higher Spin Six Vertex Model

- MathematicsMathematical Physics, Analysis and Geometry
- 2019

We consider the stochastic higher spin six vertex (SHS6V) model introduced in [Corwin-Petrov, 2016] with general integer spin parameters $I, J$. Starting from near stationary initial condition, we…

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