在原点创建粒子的半直线上随机转弯行走
Random turn walk on a half line with creation of particles at the origin
摘要：
我们考虑半晶格$ 1, 2, 3,...$上硬核粒子的随机运动，其中在每个时刻发生三种可能事件之一，即，(a)随机选择的粒子跳到空闲的相邻位置，（b）假设位置1空闲，则在原点（即，位置1）创建粒子，以及（c）假设位置1被占用，则在原点消除粒子。解释了与BKP方程的关系。也就是说，两个不同的BKP层次的tau函数分别提供生成函数（I）为不同粒子配置之间的过渡权重和（II）为一个重要的对象：一个归一化函数，它起着我们的非平衡系统的统计和的作用。作为一个例子，我们研究了一个模型，其中跳频速率取决于两个参数（$r$和$β$）。对于时间$\time\to\infty$，我们得到了从初始空态（没有粒子的状态）获得的粒子的渐近构型，并在$β=1$找到了一阶跃迁的模拟。
英文摘要：
We consider a version of random motion of hard core particles on the semi-lattice $ 1, 2, 3,...$, where in each time instant one of three possible events occurs, viz., (a) a randomly chosen particle hops to a free neighboring site, (b) a particle is created at the origin (namely, at site 1) provided that site 1 is free and (c) a particle is eliminated at the origin (provided that the site 1 is occupied). Relations to the BKP equation are explained. Namely, the tau functions of two different BKP hierarchies provide generating functions respectively (I) for transition weights between different particle configurations and (II) for an important object: a normalization function which plays the role of the statistical sum for our non-equilibrium system. As an example we study a model where the hopping rate depends on two parameters ($r$ and $β$). For time $\time\to\infty$ we obtain the asymptotic configuration of particles obtained from the initial empty state (the state without particles) and find an analog of the first order transition at $β=1$.
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