A First Look at First-Passage Processes

S. Redner

doi:10.1016/j.physa.2023.128545

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arXiv · 2201.10048

A First Look at First-Passage Processes

S. Redner

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Abstract

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.

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S. Redner. 2022-01-25. A First Look at First-Passage Processes. https://doi.org/10.1016/j.physa.2023.128545

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