论文标题
加尔顿 - 瓦特森树上的tasep
The TASEP on Galton-Watson trees
论文作者
论文摘要
我们研究在根部生成颗粒的树上完全不对称的简单排除过程（TASEP）。粒子只能从根上跳下来，它们从$ x $跳至$ y $，价格为$ r_ {x，y} $ $ y $是空的。从所有空的初始条件开始，我们表明在时间$ t $的配置分布会收敛到平衡。我们研究电流并给出过渡速率的条件，使得电流是线性秩序或零电流的，即颗粒相互阻挡。一个具有独立感兴趣的关键步骤是约束第一代，即第一代的粒子轨迹将第一个$ n $颗粒的轨迹切换。
We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from $x$ to $y$ at rate $r_{x,y}$ provided $y$ is empty. Starting from the all empty initial condition, we show that the distribution of the configuration at time $t$ converges to an equilibrium. We study the current and give conditions on the transition rates such that the current is of linear order or such that there is zero current, i.e. the particles block each other. A key step, which is of independent interest, is to bound the first generation at which the particle trajectories of the first $n$ particles decouple.
