The recombination equation for interval partitions

Baake M, Shamsara E (2017)
Monatshefte für Mathematik 182(2): 243-269.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Baake, MichaelUniBi; Shamsara, Elham
Abstract / Bemerkung
The general deterministic recombination equation in continuous time is analysed for various lattices, with special emphasis on the lattice of interval (or ordered) partitions. Based on the recently constructed (Baake et al. in Discr Cont Dynam Syst 36:63-95, 2016) general solution for the lattice of all partitions, the corresponding solution for interval partitions is derived and analysed in detail. We focus our attention on the recursive structure of the solution and its decay rates, and also discuss the solution in the degenerate cases, where it comprises products of monomials with exponentially decaying factors. This can be understood via the Markov generator of the underlying partitioning process that was recently identified. We use interval partitions to gain insight into the structure of the solution, while our general framework works for arbitrary lattices.
Stichworte
Recombination equation; Population genetics; Markov generator; Interval; partitions; Measure-valued equations; Nonlinear ODEs; Closed solution
Erscheinungsjahr
2017
Zeitschriftentitel
Monatshefte für Mathematik
Band
182
Ausgabe
2
Seite(n)
243-269
ISSN
0026-9255
eISSN
1436-5081
Page URI
https://pub.uni-bielefeld.de/record/2909445

Zitieren

Baake M, Shamsara E. The recombination equation for interval partitions. Monatshefte für Mathematik. 2017;182(2):243-269.
Baake, M., & Shamsara, E. (2017). The recombination equation for interval partitions. Monatshefte für Mathematik, 182(2), 243-269. https://doi.org/10.1007/s00605-016-1004-z
Baake, M., and Shamsara, E. (2017). The recombination equation for interval partitions. Monatshefte für Mathematik 182, 243-269.
Baake, M., & Shamsara, E., 2017. The recombination equation for interval partitions. Monatshefte für Mathematik, 182(2), p 243-269.
M. Baake and E. Shamsara, “The recombination equation for interval partitions”, Monatshefte für Mathematik, vol. 182, 2017, pp. 243-269.
Baake, M., Shamsara, E.: The recombination equation for interval partitions. Monatshefte für Mathematik. 182, 243-269 (2017).
Baake, Michael, and Shamsara, Elham. “The recombination equation for interval partitions”. Monatshefte für Mathematik 182.2 (2017): 243-269.

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