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Cutting Brownian Paths
 
Richard F. Bass University of Washington, Seattle, WA
Krzysztof Burdzy University of Washington, Seattle, WA
Front Cover for Cutting Brownian Paths
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
Front Cover for Cutting Brownian Paths
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  • Front Cover for Cutting Brownian Paths
  • Back Cover for Cutting Brownian Paths
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.

    Readership

    Graduate students and research mathematicians working in probability.

  • Table of Contents
     
     
    • 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
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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.

Readership

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
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