Strong law of large numbers for the stochastic six vertex model

2022/12/19 by Drillick, Hindy, Lin, Yier
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2212.09905

Abstract

We consider the inhomogeneous stochastic six vertex model with periodicity starting from step initial data. We prove that it converges almost surely to a deterministic limit shape. For the proof, we map the stochastic six vertex model to a deformed version of the discrete Hammersley process. Then we construct a colored version of the model and apply Liggett's superadditive ergodic theorem. The construction of the colored model includes a new idea using a Boolean-type product, which generalizes and simplifies the method used in arXiv:2204.11158.

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