Abstract
We consider the inhomogeneous stochastic six vertex model with periodic weights 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 [Sep97, BEGG16]. 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 [DL22].
Funding Statement
HD was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1644869, as well as the W.M. Keck Foundation Science and Engineering grant on “Extreme Diffusion” and the Fernholz Foundation’s Minerva summer fellows program.
Acknowledgments
We thank Ivan Corwin for suggesting the question and for helpful comments on the paper. We thank Pablo Ferrari, Amol Aggarwal, and the anonymous referee for helpful discussion and comments.
Citation
Hindy Drillick. Yier Lin. "Strong law of large numbers for the stochastic six vertex model." Electron. J. Probab. 28 1 - 21, 2023. https://doi.org/10.1214/23-EJP1041
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