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.

arXiv comment30 pages

References in corpus (5)

• Correlation functions for a strongly correlated boson system
• Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra
• Lectures on Integrable probability: Stochastic vertex models and symmetric functions
• Stochastic higher spin six vertex model and Madconald measures
• Law of Large Numbers for Infinite Random Matrices over a Finite Field

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• Two-parameter Littlewood identities and half-space Yang--Baxter random fields for stable spin Hall--Littlewood symmetric functions