We introduce a stochastic eight-vertex model motivated by the eight-vertex model in statistical mechanics. We study its invariant measures under a certain balance condition for the creation and annihilation probabilities of particles. We also discuss its scaling limits, that is, the hydrodynamic limit, and the linear and nonlinear fluctuations rather formally. We especially obtain a new type of KPZ-Burgers equation in the nonlinear limit.

中文翻译：

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随机八顶点模型、其不变测度和 KPZ 极限

我们引入了由统计力学中的八顶点模型驱动的随机八顶点模型。我们研究了它在一定平衡条件下粒子产生和湮灭概率的不变测度。我们还比较正式地讨论了它的标度极限，即流体动力学极限，以及线性和非线性波动。我们特别在非线性极限下得到了一种新型的KPZ-Burgers方程。