The Markov embedding problem with applications to reversible matrices and recombination

Date: Monday 17 November 2025

Abstract

The question whether a given Markov matrix can occur in a continuous-time Markov chain is known as the Markov interpolation or embedding problem. It is fully solved only for matrices up to dimension 4, while only partial results exist beyond that. We review the problem and some of the known results, and discuss it for reversible Markov matrices and for the partitioning process of (biological) recombination, which is important in population genetics.