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

**Sabine Jansen**

*(Leiden University)*

**Noemi Kurt**

*(TU Berlin)*

#### 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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Pages: 1-15

Publication Date: February 21, 2013

DOI: 10.1214/ECP.v18-2194

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