A Particle System on the Tree with Unusual Asymptotic Behavior
Shirin Handjani, Center for Communications Research
We consider a voter model on the tree in which the flip rates are not exactly spatially homogeneous. This process can be used to describe voting patterns in a population or tumor growth. The invariant measures and asymptotic behavior can be described rather completely. Furthermore, 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.