Summary: University of Washington Math 523A Lecture 9
Lecturer: Yuval Peres
Monday, April 27, 2009
1 Biased and unbiased random walks on Z
We first discuss some ways to approach Problem 3 from the first homework assignment. Let
St = S0 + t
j=1 Xj, where Xj
1, p
-1, q = 1 - p
are i.i.d. random variables with p 1
2
.
Let Pk and Ek denote the probability and expectation, respectively, for the process started
at S0 = k. We want to show
E0(1) =
1
2p-1
, p > 1
2
, p = 1