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

   
@article{ECP2194,
	author = {Sabine Jansen and Noemi Kurt},
	title = {Graphical representation of certain moment dualities and application to population models with balancing selection},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {18},
	year = {2013},
	keywords = {Markov processes, duality, interacting particle systems, graphical representation, annihilation, selection},
	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.
},
	pages = {no. 14, 1-15},
	issn = {1083-589X},
	doi = {10.1214/ECP.v18-2194},    
        url = {http://ecp.ejpecp.org/article/view/2194}}