The art of random walks
著者
書誌事項
The art of random walks
（Lecture notes in mathematics, 1885）
Springer, c2006
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注記
Includes bibliographical references (p. [191]-195) and index
内容説明・目次
内容説明
The main aim of this book is to reveal 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 heat diffusion at this general level and discusses the multiplicative Einstein relation; Isoperimetric inequalities; and Heat kernel estimates; Elliptic and parabolic Harnack inequality.
目次
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.
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