Hardcover ISBN:  9780821836385 
Product Code:  PSPUM/72.2 
List Price:  $128.00 
MAA Member Price:  $115.20 
AMS Member Price:  $102.40 
Electronic ISBN:  9780821893784 
Product Code:  PSPUM/72.2.E 
List Price:  $120.00 
MAA Member Price:  $108.00 
AMS Member Price:  $96.00 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 72; 2004; 574 ppMSC: Primary 28; 11; 37; 60; 68; 82;
This volume offers an excellent selection of cuttingedge 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 highquality contributions to the volume by wellknown researchers—including two articles by Mandelbrot—provide a solid crosssection 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 twopart volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.ReadershipGraduate students and research mathematicians interested in fractal geometry and its applications.
This item is also available as part of a set: 
Table of Contents

Multifractals

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  Nondegeneracy, 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 2microlocal 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 selfavoiding walk [ MR 2112127 ]

Bertrand Duplantier  Conformal fractal geometry & boundary quantum gravity [ MR 2112128 ]

Applications

Agnès Desolneux, Bernard Sapoval and Andrea Baldassarri  Selforganized percolation power laws with and without fractal geometry in the etching of random solids [ MR 2112129 ]

MarcOlivier 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 ]


RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
This volume offers an excellent selection of cuttingedge 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 highquality contributions to the volume by wellknown researchers—including two articles by Mandelbrot—provide a solid crosssection 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 twopart volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
Graduate students and research mathematicians interested in fractal geometry and its applications.

Multifractals

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  Nondegeneracy, 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 2microlocal 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 selfavoiding walk [ MR 2112127 ]

Bertrand Duplantier  Conformal fractal geometry & boundary quantum gravity [ MR 2112128 ]

Applications

Agnès Desolneux, Bernard Sapoval and Andrea Baldassarri  Selforganized percolation power laws with and without fractal geometry in the etching of random solids [ MR 2112129 ]

MarcOlivier 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 ]