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The Art of Random Walks
Paperback
Series: Lecture Notes in Mathematics, Book 1885
General MathematicsProbability & Statistics
ISBN13: 9783540330271
Publisher: Springer
Published: May 17 2006
Pages: 200
Weight: 0.67
Height: 0.45 Width: 6.14 Depth: 9.21
Language: English
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:
- The multiplicative Einstein relation,
- Isoperimetric inequalities,
- Heat kernel estimates
- Elliptic and parabolic Harnack inequality.
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