标题： 在半线上随机行走并在原点产生粒子 显示英文标题

标题： Random turn walk on a half line with creation of particles at the origin

摘要： 我们考虑在半格$ 1, 2, 3,...$上硬核粒子随机运动的一个版本，其中在每个时间点发生三种可能的事件之一，即（a）一个随机选择的粒子跳转到一个空的相邻位置，（b）如果位置1是空的，则在原点（即位置1）产生一个粒子，（c）如果位置1被占据，则在原点消除一个粒子。 与BKP方程的关系已得到解释。 具体来说，两种不同的BKP层次结构的tau函数分别提供了生成函数（I）用于不同粒子配置之间的转移权重，以及（II）用于一个重要对象：归一化函数，该函数在我们的非平衡系统中起到统计和的作用。 作为一个例子，我们研究了一个跳跃率依赖于两个参数（$r$和$\beta$）的模型。 对于时间$\time\to\infty$，我们得到了从初始空状态（无粒子的状态）获得的粒子渐近配置，并找到了在$\beta=1$处的一阶转变的类似情况。 显示英文摘要

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 $\beta$). 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 $\beta=1$.