Stochastic higher spin vertex models on the line

Stochastic higher spin vertex models on the line

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Ivan Corwin, Columbia University
Jadwin Hall 343

We show how transfer matrices of higher spin vertex models (generalizing the six-vertex model) can be conjugated into stochastic matrices describing interacting particle systems. Bethe ansatz produces eigenfunctions and we prove their completeness on the line. This, along with a self duality of the transfer matrices, provides a means to study the long time behavior of these stochastic systems. These considerations bring under one roof, all of the recently investigated integrable probabilistic systems in the Kardar-Parisi-Zhang universality class.