Dynamical stochastic higher spin vertex models

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Abstract

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 \(E_{\tau , \eta } ({\mathfrak {s}}{\mathfrak {l}}_2)\). 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 contour integral identities for observables of these models (when run under specific types of initial data) that characterize the distributions of their currents. Through asymptotic analysis of these identities in a special case, we evaluate the scaling limit for the current of a dynamical version of a discrete-time partial exclusion process. In particular, we show that its scaling exponent is 1 / 4 and that its one-point marginal converges (in a sense of moments) to that of a non-trivial random variable, which we determine explicitly.

Keywords

Dynamical stochastic higher spin vertex models Fusion Elliptic quantum group Hypergeometric series 

Mathematics Subject Classification

Primary 82B23 Secondary 60K35 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CambridgeUSA

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