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Corrigendum to: “A probabilistic analysis of a discrete-time evolution in recombination”. (English) Zbl 1469.92078

Summary: In the paper [the author, ibid. 91, 115–136 (2017; Zbl 1371.92088)] the evolution of the recombination transformation \({\Xi} = \sum_\delta \rho_\delta \bigotimes_{J \in \delta} \mu_J\) was described by a Markov chain \((Y_n)\) on a set of partitions, which converges to the finest partition. Our main results were the description of the geometric decay rate to the limit and the quasi-stationary behavior of the Markov chain when conditioned on the event that the chain does not hit the limit. All these results continue to be true, but the Markov chain \((Y_n)\) that was claimed to satisfy \(\operatorname{\Xi}^n = \mathbb{E}(\bigotimes_{J \in Y_n} \mu_J)\) required to be modified. This is done in this Corrigendum.

MSC:

92D10 Genetics and epigenetics
92D15 Problems related to evolution
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)

Citations:

Zbl 1371.92088
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References:

[1] Baake, E.; Baake, M., An exactly solved model for mutation, recombination and selection, Canad. J. Math.. Canad. J. Math., Canad. J. Math., 60, 264-265 (2008), Erratum: · Zbl 1231.92052
[2] Baake, E.; von Wangenheim, U., Single-crossover recombination and ancestral recombination trees, J. Math. Biol., 68, 6, 1371-1402 (2014) · Zbl 1284.92063
[3] Baake, E.; Baake, M.; Salamat, M., The general recombination equation in continuous time and its solution, Discrete Contin. Dyn. Syst.. Discrete Contin. Dyn. Syst., Discrete Contin. Dyn. Syst., 36, 4, 2365-2366 (2016), Erratum and addendum: · Zbl 1326.34080
[4] Martínez, S., A probabilistic analysis of a discrete-time evolution in recombination, Adv. in Appl. Math., 91, 115-136 (2017) · Zbl 1371.92088
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