**Memoirs of the American Mathematical Society**

1999;
95 pp;
Softcover

MSC: Primary 60;

Print ISBN: 978-0-8218-0968-6

Product Code: MEMO/137/657

List Price: $49.00

Individual Member Price: $29.40

**Electronic ISBN: 978-1-4704-0246-4
Product Code: MEMO/137/657.E**

List Price: $49.00

Individual Member Price: $29.40

# Cutting Brownian Paths

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*Richard F. Bass; Krzysztof Burdzy*

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 two-dimensional
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.

#### Table of Contents

# Table of Contents

## Cutting Brownian Paths

- Contents vii8 free
- 0. Introduction 112 free
- 1. Preliminaries 516 free
- 2. Decomposition of Bessel processes 718
- 3. Random walk estimates 1223
- 4. Estimates for approximate points of increase 1627
- 5. Two and three angle estimates 2334
- 6. The main estimate 3849
- 7. Estimates for wedges 6273
- 8. Filling in the gaps 8394
- 9. Further results and problems 89100
- 10. References 93104

#### Readership

Graduate students and research mathematicians working in probability.