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Cutting Brownian Paths

Richard F. Bass University of Washington, Seattle, WA
Krzysztof Burdzy University of Washington, Seattle, WA
Available Formats:
Electronic ISBN: 978-1-4704-0246-4
Product Code: MEMO/137/657.E
List Price: $49.00 MAA Member Price:$44.10
AMS Member Price: $29.40 Click above image for expanded view Cutting Brownian Paths Richard F. Bass University of Washington, Seattle, WA Krzysztof Burdzy University of Washington, Seattle, WA Available Formats:  Electronic ISBN: 978-1-4704-0246-4 Product Code: MEMO/137/657.E  List Price:$49.00 MAA Member Price: $44.10 AMS Member Price:$29.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 1371999; 95 pp
MSC: Primary 60;

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.

Graduate students and research mathematicians working in probability.

• Chapters
• 0. Introduction
• 1. Preliminaries
• 2. Decomposition of Bessel processes
• 3. Random walk estimates
• 4. Estimates for approximate points of increase
• 5. Two and three angle estimates
• 6. The main estimate
• 7. Estimates for wedges
• 8. Filling in the gaps
• 9. Further results and problems
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1371999; 95 pp
MSC: Primary 60;

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.

Graduate students and research mathematicians working in probability.

• Chapters
• 0. Introduction
• 1. Preliminaries
• 2. Decomposition of Bessel processes
• 3. Random walk estimates
• 4. Estimates for approximate points of increase
• 5. Two and three angle estimates
• 6. The main estimate
• 7. Estimates for wedges
• 8. Filling in the gaps
• 9. Further results and problems
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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