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Graphical representation of certain moment dualities and application to population models with balancing selection


 
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1. Title Title of document Graphical representation of certain moment dualities and application to population models with balancing selection
 
2. Creator Author's name, affiliation, country Sabine Jansen; Leiden University; Germany
 
2. Creator Author's name, affiliation, country Noemi Kurt; TU Berlin; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Markov processes, duality, interacting particle systems, graphical representation, annihilation, selection
 
3. Subject Subject classification 60K35
 
4. Description Abstract We investigate dual mechanisms for interacting particle systems. Generalizing an approach of Alkemper and Hutzenthaler in the case of coalescing duals, we show that a simple linear transformation leads to a moment duality of suitably rescaled processes. More precisely, we show how dualities of interacting particle systems of the form $H(A,B)=q^{|A\cap B|}, A,B\subset\{0,1\}^N, q\in[-1,1),$ are rescaled to yield moment dualities of rescaled processes. We discuss in particular the case $q=-1,$ which explains why certain population models with balancing selection have an annihilating dual process. We also consider different values of $q,$ and answer a question by Alkemper and Hutzenthaler.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) DFG project BL 1105/2-1
 
7. Date (YYYY-MM-DD) 2013-02-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2194
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2194
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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