Summary: University of Washington Math 523A
Lectures 12 and 13
Lecturer: Yuval Peres
May 8 and 11, 2009
1 More application of exploration process
We have showed that for bond percolation on b-ary tree with P = 1/b,
P(|C(root)| k)
6

k
, by using exploration process. In particular, the set of active set At where A0 =
satisfies
|At| =



0, if|At-1| = 0
|At-1| - 1 + Yt, otherwise
, where Yt and |At| are independent, Yt is the number of open neighbors of wt.
Now we suppose d = b + 1, G is a graph with n vertices and all degrees of them

Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle

Collections: Computer Technologies and Information Sciences