Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.04849

Authors: Baake, Ellen, Baake, Michael, Sumner, Jeremy

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Tasmania, Deutsche Forschungsgemeinschaft, Universität Bielefeld

Awards: G1428129756, G5747083067, G7121511148, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen

OpenAlex ID: W7211911515

Cites: 21

Cited by:

Related to: 10