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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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