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Integrability and Asymptotic Phenomena in Stochastic Vertex Models

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In this talk we describe a systematic way of producing stochastic solutions to the Yang-Baxter equation from a “base solution” that is not necessarily stochastic. This gives rise to a wide class of new families of stochastic (Markovian) vertex models with integrable weights. In various cases, these models are more amenable to algebraic analysis than are their non-stochastic counterparts, sometimes leading to new (and at times unexpected) refined asymptotic results for them. In other cases, these stochastic systems are amenable to probabilistic analysis, yielding results that seem less transparent to access algebraically and that can occasionally shed new light on the original (non-stochastic) model. This is partially based on joint work with Alexei Borodin and Alexey Bufetov.