An invitation to sample paths of Brownian motion

Peres Y.

These notes record lectures I gave at the Statistics Department, University of California, Berkeley in Spring 1998. I am grateful to the students who attended the course and wrote the first draft of the notes: Diego Garcia, Yoram Gat, Diogo A. Gomes, Charles Holton, Frederic Latremoliere, Wei Li, Ben Morris, Jason Schweinsberg, Balint Virag, Ye Xia and Xiaowen Zhou. The draft was edited by Balint Virag, Elchanan Mossel, Serban Nacu and Yimin Xiao. I thank Pertti Mattila for the invitation to lecture on this material at the joint summer school in Jyvaskyla, August 1999.