Fractals in probability and analysis

著者

• Bishop, Christopher J.
• Peres, Y. (Yuval)

書誌事項

Fractals in probability and analysis

Christopher J. Bishop, Yuval Peres

（Cambridge studies in advanced mathematics, 162）

Cambridge University Press, 2017

• : hardback

注記

Includes bibliographical references (p. 379-395) and index

内容説明・目次

内容説明

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.

目次

• 1. Minkowski and Hausdorff dimensions
• 2. Self-similarity and packing dimension
• 3. Frostman's theory and capacity
• 4. Self-affine sets
• 5. Graphs of continuous functions
• 6. Brownian motion, part I
• 7. Brownian motion, part II
• 8. Random walks, Markov chains and capacity
• 9. Besicovitch-Kakeya sets
• 10. The traveling salesman theorem
• Appendix A. Banach's fixed-point theorem
• Appendix B. Frostman's lemma for analytic sets
• Appendix C. Hints and solutions to selected exercises
• References
• Index.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB22756409
• ISBN:
  • 9781107134119
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: ix, 402 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA00109761