Here is some additional reading on random walks:
- 'Elements of the Random Walk: An introduction for Advanced Students and Researchers'
by Joseph Rudnick, George Gaspari. This is a new book on random walks.
- A survey on random walks on graphs:
L. Lovász: Random Walks on Graphs. You can find the file
- A paper by J. Cooper and J. Sprencer
on simulating random walks. Nice conjectures inside.
- A paper
by Endre Csáki, Antónia Földes, Pál Révész on a d-dimensional simple random
walk. Several open questions at the end.
- Favourite sites of simple random walk:
First, a survey
of the current status of the list of questions related to the favourite
(or: most visited) sites of simple random walk on Z, raised by P. Erdos
and P. Revesz in the early eighties.
Second, a paper
on a partial solution of one of the questions in the survey.
- A book
in preparation on random walks by Aldous and Fill. The book presents
use of random walks in the design and analysis of random algorithms
- If you are interested in use of random walks in biology:
'Random Walks in Biology' by Howard C. Berg.