The Art of Random Walks

• Main Author: Telcs, András (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Mathematics, 1885
• Subjects: Mathematics.; Partial differential equations.; Probabilities.; Probability Theory and Stochastic Processes.; Partial Differential Equations.

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 phy...

Table of Contents:

• 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.