论文标题
$ d $维的通用生存概率
Universal survival probability for a $d$-dimensional run-and-tumble particle
论文作者
论文摘要
我们考虑在$ d $尺寸中的一个主动运行粒子（RTP），并准确地计算了RTP位置的$ x $ -component的概率$ s（t）$不会更改为时间$ t $。当倒车以恒定的速度发生时，我们表明$ s（t）$在任何有限的时间$ t $的$ d $（不仅仅是大$ t $）中，这是由于著名的Sparre Sparre Andersen定理在一个维度上进行离散的随机步行。此外，我们表明，这种通用结果适用于较宽类别的RTP模型，其中每次翻滚后的粒子的速度$ v $是随机的，是由任意概率分布绘制的。因此，我们进一步证明了RTP问题中记录统计的普遍性。
We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.
