Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot, Part 2: Multifractals, Probability and Statistical Mechanics, Applications
About this Title
Michel L. Lapidus, University of California, Riverside, CA and Machiel van Frankenhuijsen, Utah Valley State College, Orem, UT, Editors
Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 2004; Volume 72.2
ISBNs: 978-0-8218-3638-5 (print); 978-0-8218-9378-4 (online)
This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers—including two articles by Mandelbrot—provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry.
In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications.
Graduate students and research mathematicians interested in fractal geometry and its applications.
Table of Contents
- Julien Barral and Benoît B. Mandelbrot – Introduction to infinite products of independent random functions (Random multiplicative multifractal measures. I) [MR 2112119]
- Julien Barral and Benoît B. Mandelbrot – Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures (Random multiplicative multifractal measures. II) [MR 2112120]
- Julien Barral – Techniques for the study of infinite products of independent random functions (Random multiplicative multifractal measures. III) [MR 2112121]
- Stéphane Jaffard – Wavelet techniques in multifractal analysis [MR 2112122]
- Jacques Lévy Véhel and Stéphane Seuret – The 2-microlocal formalism [MR 2112123]
- Jacques Peyrière – A vectorial multifractal formalism [MR 2112124]
Probability and statistical mechanics
- Ben M. Hambly and Takashi Kumagai – Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries [MR 2112125]
- Yimin Xiao – Random fractals and Markov processes [MR 2112126]
- Gregory F. Lawler, Oded Schramm and Wendelin Werner – On the scaling limit of planar self-avoiding walk [MR 2112127]
- Bertrand Duplantier – Conformal fractal geometry & boundary quantum gravity [MR 2112128]
- Agnès Desolneux, Bernard Sapoval and Andrea Baldassarri – Self-organized percolation power laws with and without fractal geometry in the etching of random solids [MR 2112129]
- Marc-Olivier Coppens – Nature inspired chemical engineering learning from the fractal geometry of nature in sustainable chemical engineering [MR 2112130]
- F. Kenton Musgrave – Fractal forgeries of nature [MR 2112131]