论文标题
随机六个顶点模型的大量法律
Strong law of large numbers for the stochastic six vertex model
论文作者
论文摘要
我们考虑从步骤初始数据开始的不均匀随机六个顶点模型。我们证明它几乎可以肯定地收敛到确定性极限形状。为了获得证明，我们将随机六个顶点模型映射到离散Hammersley过程的变形版本。然后，我们构造了该模型的彩色版本，并应用了Liggett的超脱脂性Ergodic定理。彩色模型的构建包括使用布尔型产品的新想法，该产品概括并简化了Arxiv中使用的方法：2204.11158。
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.
