Electronic Communications in Probability

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

Sabine Jansen and Noemi Kurt

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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.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 14, 15 pp.

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

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Markov processes duality interacting particle systems graphical representation annihilation selection

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Jansen, Sabine; Kurt, Noemi. Graphical representation of certain moment dualities and application to population models with balancing selection. Electron. Commun. Probab. 18 (2013), paper no. 14, 15 pp. doi:10.1214/ECP.v18-2194. https://projecteuclid.org/euclid.ecp/1465315553

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