Fractal geometry and applications: a jubilee of Benoit Mandelbrot: multifractals, probability and statistical mechanics, applications / ed. by Lapidus M.L., van Frankenhuijsen M. - Providence: American Mathematical Society, 2004. - 574 p.: ill. - (Proceedings of symposia in pure mathematics; vol.72, part.2). - ISBN 0-8218-3638-2  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Part 2. Multifractals, Probability and Statistical Mechanics, Applications Preface ........................................................ ix List of Tributes ............................................... xi MULTIFRACTALS Introduction to infinite products of independent random functions (Random multiplicative multifractal measures, Part II Julien Barral and Benoit B. Mandelbrot ....................... 3 Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures (Random multiplicative multifractal measures, Part II) Julien Barral and Benoit B. Mandelbrot ...................... 17 Techniques for the study of infinite products of independent random functions (Random multiplicative multifractal measures, Part III) Julien Barral ............................................... 53 Wavelet techniques in multifractal analysis Stephane Jaffard ............................................ 91 The 2-microlocal formalism Jacques Levy Vehel and Stephane Seuret ..................... 153 A vectorial multifractal formalism Jacques Peyriere ........................................... 217 PROBABILITY AND STATISTICAL MECHANICS Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries Ben M. Hambly and Takashi Kumagai .......................... 233 Random fractals and Markov processes Yimin Xiao ................................................. 261 On the scaling limit of planar self-avoiding walk Gregory F. Lawler, Oded Schramm, and Wendelin Werner ....... 339 Conformal fractal geometry & boundary quantum gravity Bertrand Duplantier ........................................ 365 APPLICATIONS Self-organized percolation power laws with and without fractal geometry in the etching of random solids Agnes Desolneux, Bernard Sapoval, and Andrea Baldassarri ... 485 Nature inspired chemical engineering—Learning from the fractal geometry of nature in sustainable chemical engineering Marc-Olivier Coppens ....................................... 507 Fractal forgeries of nature F. Kenton Musgrave ......................................... 533