| Issue |
ESAIM: PS
Volume 24, 2020
|
|
|---|---|---|
| Page(s) | 789 - 800 | |
| DOI | https://doi.org/10.1051/ps/2020024 | |
| Published online | 20 November 2020 | |
A basic model of mutations
1
Département de mathématiques et applications, Ecole Normale Supérieure, CNRS, PSL Research University,
75005
Paris.
2
Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris–Saclay,
91405 Orsay.
* Corresponding author: maxime.berger@ens.fr
Received:
12
March
2019
Accepted:
18
September
2020
We study a basic model for mutations. We derive exact formulae for the mean time needed to discover the master sequence, the mean returning time to the initial state, or to any Hamming class. These last two formulae are the same than the formulae obtained by Mark Kac for the Ehrenfest model.
Mathematics Subject Classification: 60J10 / 60J45 / 92D10
Key words: Markov chain / generating function / genetics / potential theory
© The authors. Published by EDP Sciences, SMAI 2020
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