Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1885)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (13 chapters)
-
Potential theory and isoperimetric inequalities
Keywords
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:
- The multiplicative Einstein relation,
- Isoperimetric inequalities,
- Heat kernel estimates
- Elliptic and parabolic Harnack inequality.
Reviews
From the reviews:
"This book studies random walks on countable infinite connected weighted graphs, with particular emphasis on fractal graphs like the Sierpinski triangular graph or the weighted Vicsek tree. … The book is intended to be self-contained and accessible to graduate and Ph.D. students. It contains a wealth of references, also on various aspects of random walks not covered by the text." (Wolfgang König, Mathematical Reviews, Issue 2007 d)
"This book studies random walks on countable infinite connected weighted graphs, with particular emphasis on fractal graphs like the Sierpinski triangular graph or the weighted Vicsek tree. … The book is intended to be self-contained and accessible to graduate and PhD students. It contains a wealth of references, also on various aspects of random walks not covered by the text. At the end of the book a list of some dozens of types of inequalities appear that are introduced in the book" (Wolfgang König, Zentralblatt MATH, Vol. 1104 (6), 2007)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: The Art of Random Walks
Authors: András Telcs
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b134090
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Softcover ISBN: 978-3-540-33027-1Published: 17 May 2006
eBook ISBN: 978-3-540-33028-8Published: 18 October 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VII, 200
Topics: Probability Theory and Stochastic Processes, Partial Differential Equations