The Art of Random Walks (Google eBook)

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Springer Science & Business Media, May 17, 2006 - Mathematics - 195 pages
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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.

 

  

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Contents

I
1
II
7
III
22
IV
23
V
49
VI
61
VII
68
VIII
71
X
95
XI
130
XII
153
XIII
164
XIV
169
XV
181
XVI
189
XVII
191

IX
82

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About the author (2006)

András Telcs is associated professor of the Budapest University of Technology. Formerly he taught statistics in business schools as well as worked for major libraries. His main research interests are random walks, discrete potential theory, active on different application of probability and statistics.