Symmetric elliptic functions, IRF models, and dynamic exclusion processes

@article{Borodin2017SymmetricEF,
  title={Symmetric elliptic functions, IRF models, and dynamic exclusion processes},
  author={Alexei Borodin},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
  • A. Borodin
  • Published 18 January 2017
  • Mathematics
  • arXiv: Mathematical Physics
We introduce stochastic Interaction-Round-a-Face (IRF) models that are related to representations of the elliptic quantum group $E_{\tau,\eta}(sl_2)$. For stochasic IRF models in a quadrant, we evaluate averages for a broad family of observables that can be viewed as higher analogs of $q$-moments of the height function for the stochastic (higher spin) six vertex models. In a certain limit, the stochastic IRF models degenerate to (1+1)d interacting particle systems that we call dynamic ASEP and… 
View PDF on arXiv
17 Citations
Background Citations
2
Methods Citations
3
Results Citations
1

17 Citations

Citation Type

Citation Type

Dynamical stochastic higher spin vertex models
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 ,…
Coloured stochastic vertex models and their spectral theory
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: …
Stochastic PDE limit of the dynamic ASEP
We study a stochastic PDE limit of the height function of the dynamic asymmetric simple exclusion process (dynamic ASEP). A degeneration of the stochastic Interaction Round-a-Face (IRF) model of…
Nonsymmetric Macdonald polynomials via integrable vertex models
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…
YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS
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…
A class of partition functions associated with Eτ,ηgl3 by Izergin–Korepin analysis
Recently, a class of partition functions associated with higher rank rational and trigonometric integrable models were introduced by Foda and Manabe. We use the dynamical R-matrix of the elliptic…
Dualities in quantum integrable many-body systems and integrable probabilities. Part I
Abstract In this study we map the dualities observed in the framework of integrable probabilities into the dualities familiar in a realm of integrable many-body systems. The dualities between the…
Time evolution of the Kardar-Parisi-Zhang equation
The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The…
Elliptic supersymmetric integrable model and multivariable elliptic functions
We investigate the elliptic integrable model introduced by Deguchi and Martin, which is an elliptic extension of the Perk-Schultz model. We introduce and study a class of partition functions of the…
Dynamic ASEP, duality and continuous $q^{-1}$-Hermite polynomials
We demonstrate a Markov duality between the dynamic ASEP and the standard ASEP. We then apply this to step initial data, as well as a half-stationary initial data (which we introduce). While…
...
...

References

SHOWING 1-10 OF 39 REFERENCES
Lectures on Integrable Probability: stochastic vertex models and symmetric functions
We consider a homogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the…
Higher spin six vertex model and symmetric rational functions
We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and…
Stochastic Higher Spin Vertex Models on the Line
We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain…
Six-vertex models and the GUE-corners process
In this paper we consider a class of probability distributions on the six-vertex model from statistical mechanics, which originate from the higher spin vertex models of…
The ASEP and Determinantal Point Processes
We introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line, with correlation kernels defined via spectral projections for the associated Jacobi…
On a family of symmetric rational functions
From duality to determinants for q-TASEP and ASEP
We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP).…
Stochastic higher spin six vertex model and q-TASEPs
Exactly solvable SOS models: local height probabilities and theta function identities
Phase transitions in the ASEP and stochastic six-vertex model
In this paper we consider two models in the Kardar-Parisi-Zhang (KPZ) universality class, the asymmetric simple exclusion process (ASEP) and the stochastic six-vertex model. We introduce a new class…
...
...