Probability Seminar: Exponential growth of ponds in invasion percolation on regular trees
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In invasion percolation, the edges of a graph are assigned i.i.d. edge
weights, and an infinite cluster is grown by recursively adding the
boundary edge of minimal weight. By considering the edges whose weight
is larger than all subsequently accepted weights, the invasion cluster
is divided into a chain of ponds linked by outlets.
Working on the regular tree, we show that the sizes of the ponds grow exponentially, with law of large numbers, central limit theorem and large deviation results, and also give asymptotics for the size of a fixed pond.
We compare with known results for Z^2 and explore why these results should be expected on more general graphs.
Working on the regular tree, we show that the sizes of the ponds grow exponentially, with law of large numbers, central limit theorem and large deviation results, and also give asymptotics for the size of a fixed pond.
We compare with known results for Z^2 and explore why these results should be expected on more general graphs.
Additional Information
Jesse Goodman (UBC)
