The Art of Random Walks (Lecture Notes in Mathematics) 〈Vol. 1885〉

Telcs, Andras

Springer（2006/06発売）

Springer（2006/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 200 p.
• 商品コード 9783540330271

基本説明

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.

Full Description

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.