非均匀半无限排斥系统中最左侧粒子的动力学
Dynamics of the leftmost particle in heterogeneous semi-infinite exclusion systems
AI总结：
研究半无限排斥粒子系统中最左侧粒子的行为，通过跳跃率条件判断其常返或瞬态，并利用M/G/∞排队比较等方法分析瞬态逃逸速率，发现最左侧粒子可呈现零常返、正常返、弹道瞬态或次扩散瞬态，且初始条件影响动力学。
摘要：
我们研究半无限粒子系统在$\mathbb{Z}$上的最左侧粒子的行为，其中每个粒子进行连续时间最近邻随机游走，具有粒子特定的跳跃速率，并受排斥相互作用（即每个位置最多一个粒子）。我们根据系统的跳跃速率给出最左侧粒子是常返或瞬态的条件，并开发工具研究其在瞬态情况下的逃逸速率，包括通过与$M/G/\infty$排队进行比较。特别地，我们展示了最左侧粒子可以是零常返、正常返、弹道瞬态或次扩散瞬态的例子。最后，我们指出了初始条件在决定动力学中的作用，并表明，例如，从密堆积初始配置出发可能发生次弹道瞬态，但从平稳初始条件出发则不会。
英文摘要：
We study the behaviour of the leftmost particle in a semi-infinite particle system on $\mathbb{Z}$, where each particle performs a continuous-time nearest-neighbour random walk, with particle-specific jump rates, subject to the exclusion interaction (i.e., no more than one particle per site). We give conditions, in terms of the jump rates on the system, under which the leftmost particle is recurrent or transient, and develop tools to study its rate of escape in the transient case, including by comparison with an $M/G/\infty$ queue. In particular we show examples in which the leftmost particle can be null recurrent, positive recurrent, ballistically transient, or subdiffusively transient. Finally we indicate the role of the initial condition in determining the dynamics, and show, for example, that sub-ballistic transience can occur started from close-packed initial configurations but not from stationary initial conditions.
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