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2013 Graphical representation of certain moment dualities and application to population models with balancing selection
Sabine Jansen, Noemi Kurt
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Electron. Commun. Probab. 18: 1-15 (2013). DOI: 10.1214/ECP.v18-2194

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.

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Sabine Jansen. Noemi Kurt. "Graphical representation of certain moment dualities and application to population models with balancing selection." Electron. Commun. Probab. 18 1 - 15, 2013. https://doi.org/10.1214/ECP.v18-2194

Information

Accepted: 21 February 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1335.60183
MathSciNet: MR3033597
Digital Object Identifier: 10.1214/ECP.v18-2194

Subjects:
Primary: 60K35

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