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Asymptotics for critical threshold growthMathematical Physics & Probability
|Speaker: ||Janko Gravner, Mathematics, UC Davis|
|Location: ||693 Kerr Hall|
|Start time: ||Tue, Oct 26 1999, 4:10PM|
Assume that a cellular automaton (CA)
rule enlarges subsets of the two--dimensional lattice, and does so
in such a way that a larger set results in a larger outcome.
Such models are called monotone solidification CA.
In the critical case, these dynamics
cannot cover the lattice starting from
any finite set, but are able to do so from
any set with finite complement. We assume that the initial
set is a product measure with a small density,
and address various scaling laws for the first passage
time to the origin, emergence of shapes, and the ability
of the dynamics toovercome pollution of space.