Between the stochastic six vertex model and Hall-Littlewood processes

Abstract

We prove that the joint distribution of the values of the height function for the stochastic six vertex model in a quadrant along a down-right path coincides with that for the lengths of the first columns of partitions distributed according to certain Hall-Littlewood processes. In the limit when one of the quadrant axes becomes continuous, we also show that the two-dimensional random field of the height function values has the same distribution as the lengths of the first columns of partitions from certain ascending Hall-Littlewood processes evolving under a Robinson-Schensted-Knuth type Markovian evolution.

30 pages

References in corpus (1)

• Stochastic higher spin six vertex model and Madconald measures

Cited by in corpus (2)

• Refined dual Grothendieck polynomials, integrability, and the Schur measure
• Stable spin Hall-Littlewood symmetric functions, combinatorial identities, and half-space Yang-Baxter random field