Fractals in Probability and Analysis (Cambridge Studies in Advanced Mathematics) - Hardcover

Christopher J. Bishop , Yuval Peres

Hardcover

ISBN 10: 1107134110 ISBN 13: 9781107134119

Publisher: Cambridge University Press, 2016

Synopsis

This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem. The broad range of techniques presented enables key ideas to be highlighted, without the distraction of excessive technicalities. The authors incorporate some novel proofs which are simpler than those available elsewhere. Where possible, chapters are designed to be read independently so the book can be used to teach a variety of courses, with the clear structure offering students an accessible route into the topic.

About this title

About the Author

Christopher J. Bishop is a professor in the Department of Mathematics at Stony Brook University, New York. He has made contributions to the theory of function algebras, Kleinian groups, harmonic measure, conformal and quasiconformal mapping, holomorphic dynamics and computational geometry. Yuval Peres is a Principal Researcher at Microsoft Research in Redmond, Washington. He is particularly known for his research in topics such as fractals and Hausdorff measures, random walks, Brownian motion, percolation and Markov chain mixing times.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2016
• Language: English
• ISBN 10: 1107134110
• ISBN 13: 9781107134119
• Binding: Hardcover
• Edition number: 1
• Number of pages: 418