A Particle System on the Tree with Unusual Asymptotic Behavior

S.J. Handjani

2009, v.15, №4, 477-492

ABSTRACT

We consider voter models on regular trees in which the flip rates are not spatially homogeneous. The invariant measures and asymptotic behavior of these processes can often be described rather completely. Furthermore, for degree three, the model has an intriguing property in the sense that even a slight increase in the birth rate at the origin causes dramatic changes in the limiting distributions. In particular, we show that for any $q>1$, $0 < p < 1$, if we increase the birth rate at the origin by a factor of $q$ there are initial distributions for which this increase causes the limiting distribution to change from probability p of a site being occupied to probability 1 of a site being occupied.

Keywords: voter models,random walks,spatially inhomogeneous,survival

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