# Cutting Brownian Paths

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*Richard F. Bass; Krzysztof Burdzy*

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