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PreprintarXiv licencearXiv

Recombination in discrete and continuous time from the viewpoint of Markov embedding

  • Ellen Baake
  • Michael Baake
  • Jeremy Sumner
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Abstract

The classic recombination equation, both in discrete and in continuous time, can be solved in a way that derives from the Markov chain of a partitioning process. Here, we revisit this structure from the point of view of the Markov embedding problem. In particular, we analyse when a discrete-time Markov matrix of recombination type can occur in a time-homogeneous Markov semigroup that is generated by a recombination rate matrix. En route, we also show that such rate matrices (or Markov generators) generally do not form a matrix algebra, but span a real Lie algebra.

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Cite

BibTeXRIS
BibTeX
@misc{baake2026recombination,
  title = {{Recombination in discrete and continuous time from the viewpoint of Markov embedding}},
  author = {Ellen Baake and Michael Baake and Jeremy Sumner},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04849},
  eprint = {2609.04849},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04849},
}
RIS
TY  - UNPB
TI  - Recombination in discrete and continuous time from the viewpoint of Markov embedding
AU  - Ellen Baake
AU  - Michael Baake
AU  - Jeremy Sumner
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.04849
UR  - https://arxiv.org/abs/2609.04849
AB  - The classic recombination equation, both in discrete and in continuous time, can be solved in a way that derives from the Markov chain of a partitioning process. Here, we revisit this structure from the point of view of the Markov embedding problem. In particular, we analyse when a discrete-time Markov matrix of recombination type can occur in a time-homogeneous Markov semigroup that is generated by a recombination rate matrix. En route, we also show that such rate matrices (or Markov generators) generally do not form a matrix algebra, but span a real Lie algebra.
ER  -