Memoirs of the American Mathematical Society 1999; 95 pp; softcover Volume: 137 ISBN10: 0821809687 ISBN13: 9780821809686 List Price: US$46 Individual Members: US$27.60 Institutional Members: US$36.80 Order Code: MEMO/137/657
 A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? Let \(Z_t\) be twodimensional Brownian motion. Say that a straight line \(\mathcal L\) is a cut line if there exists a time \(t \in (0,1)\) such that the trace of \(\{ Z_s: 0 \leq s < t\}\) lies on one side of \(\mathcal L\) and the trace of \(\{Z_s: t < s < 1\}\) lies on the other side of \(\mathcal L\). In this volume, the authors provide a solution, discuss related works, and present a number of open problems. Readership Graduate students and research mathematicians working in probability. Table of Contents  Introduction
 Preliminaries
 Decomposition of Bessel processes
 Random walk estimates
 Estimates for approximate points of increase
 Two and three angle estimates
 The main estimate
 Estimates for wedges
 Filling in the gaps
 Further results and problems
 References
