Symmetric elliptic functions, IRF models, and dynamic exclusion processes

  • Alexei Borodin

    Massachusetts Institute of Technology (MIT), Cambridge, USA
Symmetric elliptic functions, IRF models, and dynamic exclusion processes cover

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Abstract

We introduce stochastic Interaction-Round-a-Face (IRF) models that are related to representations of the elliptic quantum group . For stochastic IRF models in a quadrant, we evaluate averages for a broad family of observables that can be viewed as higher analogs of -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 SSEP; their jump rates depend on local values of the height function. For the step initial condition, we evaluate averages of observables for them as well, and use those to investigate one-point asymptotics of the dynamic SSEP.

The construction and proofs are based on remarkable properties (branching and Pieri rules, Cauchy identities) of a (seemingly new) family of symmetric elliptic functions that arise as matrix elements in an infinite volume limit of the algebraic Bethe ansatz for .

Cite this article

Alexei Borodin, Symmetric elliptic functions, IRF models, and dynamic exclusion processes. J. Eur. Math. Soc. 22 (2020), no. 5, pp. 1353–1421

DOI 10.4171/JEMS/947