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A Particle System on the Tree with Unusual Asymptotic Behavior
Shirin Handjani, Center for Communications Research
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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.