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. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
Multifractals: Introduction to infinite products of independent random functions (Random multiplicative multifractal measures, part I) by J. Barral and B. B. Mandelbrot Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures (Random multiplicative multifractal measures, part II) by J. Barral and B. B. Mandelbrot Techniques for the study of infinite products of independent random functions (Random multiplicative multifractal measures, part III) by J. Barral Wavelet techniques in multifractal analysis by S. P. Jaffard The 2-microlocal formalism by J. L. Vehel and S. Seuret A vectorial multifractal formalism by J. Peyriere Probability and statistical mechanics: Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries by B. M. Hambly and T. Kumagai Random fractals and Markov processes by Y. Xiao On the scaling limit of planar self-avoiding walk by G. F. Lawler, O. Schramm, and W. Werner Conformal fractal geometry & boundary quantum gravity by B. Duplantier Applications: Self-organized percolation power laws with and without fractal geometry in the etching of random solids by A. Desolneux, B. Sapoval, and A. Baldassarri Nature inspired chemical engineering-Learning from the fractal geometry of nature in sustainable chemical engineering by M.-O. Coppens Fractal forgeries of nature by F. K. Musgrave.