A First Look at First-Passage Processes
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917890199912448 |
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| author | Redner, S. |
| author_facet | Redner, S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_10048 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A First Look at First-Passage Processes Redner, S. Statistical Mechanics Probability 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. |
| title | A First Look at First-Passage Processes |
| topic | Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2201.10048 |