论文标题
首先看第一分行过程
A First Look at First-Passage Processes
论文作者
论文摘要
这些笔记是基于我在2021年Bruneck Summer School（实际上）关于第一步过程和基本理论的某些应用的讲座。我首先定义了什么是第一步过程，并介绍了第一通道概率和熟悉的职业概率之间的联系。然后，讨论了半无限线和有限间隔的第一段的一些基本特征，例如分裂概率和第一页的时间。我还处理第一通道和静电之间的基本联系。然后提出了许多第一通道过程的应用，包括在大于两个维度的球体中的命中率，反应速率理论及其扩展到细胞表面上的受体，在二维中的无限吸收楔形内，在二维中吸收楔形，在一个维度中的随机狩猎过程中，在一个尺寸的范围内，在扩展过程中的生存，并在扩展的范围内的生存，最终是在扩展的范围内的生存。
These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the connection between the first-passage probability and the familiar occupation probability. Some basic features of first passage on the semi-infinite line and a finite interval are then discussed, such as splitting probabilities and first-passage times. I also treat the fundamental connection between first passage and electrostatics. A number of applications of first-passage processes are then presented, including the hitting probability for a sphere in greater than two dimensions, reaction rate theory and its extension to receptors on a cell surface, first-passage inside an infinite absorbing wedge in two dimensions, stochastic hunting processes in one dimension, the survival of a diffusing particle in an expanding interval, and finally the dynamics of the classic birth-death process.
