Dual Families of Interacting Particle Systems on Graphs |
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Authors: | Aidan Sudbury |
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Institution: | (1) Department of Mathematics and Statistics, Monash University, Clayton, Victoria, 3800, Australia |
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Abstract: | A simple condition for IPS (Interacting Particle Systems) with nearest neighbor interactions to be self-dual is given. It follows that any IPS with the contact transition and no spontaneous birth is self-dual. It is shown that families of IPS exist in which every IPS is dual to every other, and such that for every pair of IPS, one is a thinning of the other. Further, all such IPS have the same form for an equilibrium distribution when expressed in terms of survival probabilities. Convergence results from a wide class of initial infinite measures follow. |
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Keywords: | Interacting Particle Systems duality |
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