A basic model of mutations
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 789-800

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.

DOI : 10.1051/ps/2020024
Classification : 60J10, 60J45, 92D10
Keywords: Markov chain, generating function, genetics, potential theory 
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     author = {Berger, Maxime and Cerf, Rapha\"el},
     title = {A basic model of mutations},
     journal = {ESAIM: Probability and Statistics},
     pages = {789--800},
     year = {2020},
     publisher = {EDP Sciences},
     volume = {24},
     doi = {10.1051/ps/2020024},
     mrnumber = {4177357},
     zbl = {1455.60094},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2020024/}
}
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Berger, Maxime; Cerf, Raphaël. A basic model of mutations. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 789-800. doi: 10.1051/ps/2020024

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