Brownian Motion and its Applications to Mathematical Analysis

École d'Été de Probabilités de Saint-Flour XLIII – 2013

  • Krzysztof Burdzy

Part of the Lecture Notes in Mathematics book series (LNM, volume 2106)

Also part of the École d'Été de Probabilités de Saint-Flour book sub series (LNMECOLE, volume 2106)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Krzysztof Burdzy
    Pages 1-10
  3. Krzysztof Burdzy
    Pages 11-19
  4. Krzysztof Burdzy
    Pages 21-29
  5. Krzysztof Burdzy
    Pages 31-39
  6. Krzysztof Burdzy
    Pages 41-62
  7. Krzysztof Burdzy
    Pages 63-75
  8. Krzysztof Burdzy
    Pages 77-87
  9. Krzysztof Burdzy
    Pages 89-96
  10. Krzysztof Burdzy
    Pages 97-105
  11. Back Matter
    Pages 133-140

About this book


These lecture notes provide an introduction to the applications of Brownian motion to analysis and, more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics.
The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains.


"hot spots" conjecture 60J65, 60H30, 60G17 Brownian motion Neumann eigenfunction coupling heat equation

Authors and affiliations

  • Krzysztof Burdzy
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04393-7
  • Online ISBN 978-3-319-04394-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book