 
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 bary 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, ifAt1 = 0
At1  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
