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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Sudbury, A. Dual Families of Interacting Particle Systems on Graphs. Journal of Theoretical Probability 13, 695–716 (2000). https://doi.org/10.1023/A:1007806427774
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DOI: https://doi.org/10.1023/A:1007806427774