Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Quelques Interactions Entre Analyse, Probabilités et Fractals
 
J. Barral Université Paris 13, Villetaneuse, France
J. Berestycki Université Pierre et Marie Curie, Paris, France
J. Bertoin Université Pierre et Marie Curie, Paris, France
A. H. Fan Université de Picardie, Amiens, France
B. Haas Université Paris-Dauphine, Paris, France
S. Jaffard Université Paris Est Créteil, France
G. Miermont Université Paris-Sud Bâtiment, Orsay, France
J. Peyrière Université Paris-Sud 11, Orsay, France
A publication of the Société Mathématique de France
Quelques Interactions Entre Analyse, Probabilites et Fractals
Softcover ISBN:  978-2-85629-313-3
Product Code:  PASY/32
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
Quelques Interactions Entre Analyse, Probabilites et Fractals
Click above image for expanded view
Quelques Interactions Entre Analyse, Probabilités et Fractals
J. Barral Université Paris 13, Villetaneuse, France
J. Berestycki Université Pierre et Marie Curie, Paris, France
J. Bertoin Université Pierre et Marie Curie, Paris, France
A. H. Fan Université de Picardie, Amiens, France
B. Haas Université Paris-Dauphine, Paris, France
S. Jaffard Université Paris Est Créteil, France
G. Miermont Université Paris-Sud Bâtiment, Orsay, France
J. Peyrière Université Paris-Sud 11, Orsay, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-313-3
Product Code:  PASY/32
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Panoramas et Synthèses
    Volume: 322010; 243 pp
    MSC: Primary 11; 26; 28; 37; 43; 60;

    Following the seminal contributions of Benoît Mandelbrot in the 1970s, concepts derived from fractal geometry gave a new impulse to several areas of mathematics. The goal of this volume is to present syntheses on two subjects where important advances occurred in the last 15 years: multiplicative processes and fragmentation. One arose from harmonic analysis (Riesz products) and the other from a probabilistic model proposed by N. Kolmogorov to explain experimental observations on rock fragmentation. However, they share analogies and use common mathematical tools issued from the study of random fractals.

    The first paper introduces basic concepts in fractal analysis. It starts with the description of the historical developments that led to their introduction and interactions. The definitions of fractional dimensions are introduced, and pertinent tools in geometric measure theory are recalled. Examples of multifractal functions and measures are studied. Finally, ubiquity systems, which play an increasing role in multifractal analysis, are introduced.

    The second paper deals with fine geometric properties of measures obtained as limits of multiplicative processes. It starts by showing in which contexts they appear and by describing their key properties. The notions of dimension of a measure and of multifractal analysis are introduced in a general setting and illustrated on the aforementioned examples. Finally, the efficiency of these measures for the description of percolation on trees, and for dynamical or random coverings, is shown.

    The third paper describes the time evolution of objects that disaggregate in a random way, and the fragments of which evolve independently. A statistical self-similarity assumption endows them with a structure of random fractal. The foundations of fragmentation theory are given, and the laws of these processes are shown to be characterized by a self-similarity index, a dislocation measure, and an erosion coefficient. Then, a random tree endowed with a distance is considered, which leads to a description of the genealogy of the process. Finally, the speed with which the fragment containing a given point decays is studied. This leads to the introduction of a multifractal spectrum of speeds of fragmentation.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 322010; 243 pp
MSC: Primary 11; 26; 28; 37; 43; 60;

Following the seminal contributions of Benoît Mandelbrot in the 1970s, concepts derived from fractal geometry gave a new impulse to several areas of mathematics. The goal of this volume is to present syntheses on two subjects where important advances occurred in the last 15 years: multiplicative processes and fragmentation. One arose from harmonic analysis (Riesz products) and the other from a probabilistic model proposed by N. Kolmogorov to explain experimental observations on rock fragmentation. However, they share analogies and use common mathematical tools issued from the study of random fractals.

The first paper introduces basic concepts in fractal analysis. It starts with the description of the historical developments that led to their introduction and interactions. The definitions of fractional dimensions are introduced, and pertinent tools in geometric measure theory are recalled. Examples of multifractal functions and measures are studied. Finally, ubiquity systems, which play an increasing role in multifractal analysis, are introduced.

The second paper deals with fine geometric properties of measures obtained as limits of multiplicative processes. It starts by showing in which contexts they appear and by describing their key properties. The notions of dimension of a measure and of multifractal analysis are introduced in a general setting and illustrated on the aforementioned examples. Finally, the efficiency of these measures for the description of percolation on trees, and for dynamical or random coverings, is shown.

The third paper describes the time evolution of objects that disaggregate in a random way, and the fragments of which evolve independently. A statistical self-similarity assumption endows them with a structure of random fractal. The foundations of fragmentation theory are given, and the laws of these processes are shown to be characterized by a self-similarity index, a dislocation measure, and an erosion coefficient. Then, a random tree endowed with a distance is considered, which leads to a description of the genealogy of the process. Finally, the speed with which the fragment containing a given point decays is studied. This leads to the introduction of a multifractal spectrum of speeds of fragmentation.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.