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Stochastic symplectic ice

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Abstract

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term “stochastic symplectic ice”. The models consist of alternating rows of two types of vertices. The probabilistic interpretation of the models leads to novel interacting particle systems where particles alternately jump to the right and then to the left. Two colored versions of the models and related stochastic dynamics are also introduced. Using the Yang–Baxter equations, we establish functional equations and recursive relations for the partition functions of these models. In particular, the recursive relations satisfied by the partition function of one of the colored models are closely related to Demazure–Lusztig operators of type C.

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Acknowledgements

The author wishes to thank Daniel Bump for his encouragement and many helpful conversations. The author thanks Valentin Buciumas, Nathan Gray, Slava Naprienko, and Travis Scrimshaw for their helpful comments, and Ben Brubaker for his help. The author thanks Kohei Motegi for bringing the reference [43] to his attention. Additionally, the author thanks the anonymous referees for their helpful comments.

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  1. Department of Statistics, Stanford University, 390 Jane Stanford Way, Stanford, CA, 94305-4020, USA

    Chenyang Zhong

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Zhong, C. Stochastic symplectic ice. Lett Math Phys 112, 55 (2022). https://doi.org/10.1007/s11005-022-01547-w

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