Between the stochastic six vertex model and Hall-Littlewood processes

2016/11/29 by Alexei Borodin, Borodin, Alexei, Alexey Bufetov +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1611.09486

openalex publication_date 2016/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• 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

Cited by

• Free boundary q-Whittaker and Hall-Littlewood processes

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