We consider the persistent exclusion process in which a set of persistent random walkers interact via hard-core exclusion on a hypercubic lattice in $d$ dimensions. We work within the ballistic regime whereby particles continue to hop in the same direction over many lattice sites before reorienting. In the case of two particles, we find the mean first-passage time to a jammed state where the particles occupy adjacent sites and face each other. This is achieved within an approximation that amounts to embedding the one-dimensional system in a higher-dimensional reservoir. Numerical results demonstrate the validity of this approximation, even for small lattices. The results admit a straightforward generalisation to dilute systems comprising more than two particles. A self-consistency condition on the validity of these results suggest that clusters may form at arbitrarily low densities in the ballistic regime, in contrast to what has been found in the diffusive limit.

中文翻译：

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任意空间维度中多个持久性随机游走器的干扰

我们考虑持续排除过程，其中一组持续随机游走者通过 $d$ 维的超立方晶格上的硬核排除进行交互。我们在弹道机制内工作，即粒子在重新定向之前继续在许多晶格点上以相同方向跳跃。在两个粒子的情况下，我们找到了粒子占据相邻位置并彼此面对的阻塞状态的平均首次通过时间。这是在近似值内实现的，相当于将一维系统嵌入到更高维的储层中。数值结果证明了这种近似的有效性，即使对于小格子也是如此。结果承认对包含两个以上粒子的稀释系统的直接概括。