论文标题
第一阶段驱动的边界衰退
First-Passage-Driven Boundary Recession
论文作者
论文摘要
我们研究了在半无限线上的布朗粒子的移动边界问题，其中边界与粒子连续碰撞与边界之间的时间成正比移动。现象学上丰富的动态出现了。特别是，粒子首先到达$ n^\ text {th} $ time缩放为$ t^{ - （1+2^{ - n}）} $的概率。由于该分布的尾巴变得越来越胖，因此连续的第一段段落之间的典型时间会越来越长。我们还发现，粒子和边界尺度之间的碰撞数为$ \ ln \ ln t $，而边界位置的时间依赖性则为$ t/\ ln t $。
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically rich dynamics arises. In particular, the probability for the particle to first reach the moving boundary for the $n^\text{th}$ time asymptotically scales as $t^{-(1+2^{-n})}$. Because the tail of this distribution becomes progressively fatter, the typical time between successive first passages systematically gets longer. We also find that the number of collisions between the particle and the boundary scales as $\ln\ln t$, while the time dependence of the boundary position varies as $t/\ln t$.
