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Corrigendum to: “A probabilistic analysis of a discrete-time evolution in recombination”. (English) Zbl 07116117
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:
 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 92D10 Genetics and epigenetics
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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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