The Art of Random Walks

  • András Telcs

Part of the Lecture Notes in Mathematics book series (LNM, volume 1885)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Potential theory and isoperimetric inequalities

  3. Local theory

    1. Front Matter
      Pages 70-70
    2. Pages 83-93
    3. Pages 95-129
    4. Pages 131-151
    5. Pages 153-163
    6. Pages 165-168
    7. Pages 181-185
  4. Back Matter
    Pages 187-199

About this book


Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics:

    1. The multiplicative Einstein relation,
    2. Isoperimetric inequalities,
    3. Heat kernel estimates
    4. Elliptic and parabolic Harnack inequality.



Brownian motion diffusion heat kernel isoperimetric inequalities random walk reversible Markov chain

Authors and affiliations

  • András Telcs
    • 1
  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology, Electrical Engineering and Informatics1117BudapestHungary

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