Art of Random Walks

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.

• Potential theory and isoperimetric inequalities.- Basic definitions and preliminaries.- Some elements of potential theory.- Isoperimetric inequalities.- Polynomial volume growth.- Local theory.- Motivation of the local approach.- Einstein relation.- Upper estimates.- Lower estimates.- Two-sided estimates.- Closing remarks.- Parabolic Harnack inequality.- Semi-local theory.

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)