Translator Disclaimer
2019 A spectral decomposition for a simple mutation model
Martin Möhle
Electron. Commun. Probab. 24: 1-14 (2019). DOI: 10.1214/19-ECP222

Abstract

We consider a population of $N$ individuals. Each individual has a type belonging to some at most countable type space $K$. At each time step each individual of type $k\in K$ mutates to type $l\in K$ independently of the other individuals with probability $m_{k,l}$. It is shown that the associated empirical measure process is Markovian. For the two-type case $K=\{0,1\}$ we derive an explicit spectral decomposition for the transition matrix $P$ of the Markov chain $Y=(Y_n)_{n\ge 0}$, where $Y_n$ denotes the number of individuals of type $1$ at time $n$. The result in particular shows that $P$ has eigenvalues $(1-m_{0,1}-m_{1,0})^i$, $i\in \{0,\ldots ,N\}$. Applications to mean first passage times are provided.

Citation

Download Citation

Martin Möhle. "A spectral decomposition for a simple mutation model." Electron. Commun. Probab. 24 1 - 14, 2019. https://doi.org/10.1214/19-ECP222

Information

Received: 11 August 2018; Accepted: 26 February 2019; Published: 2019
First available in Project Euclid: 21 March 2019

zbMATH: 1412.60106
MathSciNet: MR3933039
Digital Object Identifier: 10.1214/19-ECP222

Subjects:
Primary: 15A18‎, 60J10
Secondary: 60J45, 92D10

JOURNAL ARTICLE
14 PAGES


SHARE
Back to Top