We consider current statistics for a two-species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green’s function as well as for a joint current distribution of the model, and study its long time behavior. For a step-type initial condition, we show that the limiting distribution is a product of the Gaussian and the Gaussian unitary ensemble Tracy-Widom distributions. This is the first analytic confirmation for a multicomponent system of a prediction from the recently proposed nonlinear fluctuating hydrodynamics for one-dimensional systems.

中文翻译：

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一类两种物种排斥过程的一维非线性波动流体动力学的精确确认

我们考虑对一维晶格上相反方向跳跃的粒子的两种物种排斥过程的当前统计数据。我们推导了格林函数以及模型的联合电流分布的精确公式，并研究了其长时间行为。对于阶跃型初始条件，我们证明了极限分布是高斯和高斯unit整体系特雷西-维多姆分布的乘积。这是对多分量系统的预测的首次分析确认，该预测是根据最近提出的针对一维系统的非线性波动流体动力学进行的。