The Art of Random Walks / by András Telcs.

Format:

Book

Author/Creator:

Telcs, András, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1885.

Lecture Notes in Mathematics, 0075-8434 ; 1885

Language:

English

Subjects (All):

Distribution (Probability theory).

Differential equations, Partial.

Probability Theory and Stochastic Processes.

Partial Differential Equations.

Local Subjects:

Probability Theory and Stochastic Processes.

Partial Differential Equations.

Physical Description:

1 online resource (VII, 200 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.

System Details:

text file PDF

Summary:

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. .

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.

Other Format:

Printed edition:

ISBN:

9783540330288

Access Restriction:

Restricted for use by site license.