Benoit B. MANDELBROT
 
 

Benoit Mandelbrot

NEGATIVE FRACTAL DIMENSION

Negative Holding and Divergent Moments

 

VIRTUAL SELECTA

 

 

 

 

This open-ended virtual book will be compiled
and extended as needs and opportunities arise.
It consists in links to the author’s
publications on negative fractal dimension
that are found on this home site
http://www.math.yale.edu/mandelbrot


TABLE OF CONTENTS

  123

WWW M. M 1989e. A class of multifractal measures with negative (latent) values for the “dimension” f(a)). Fractals’ Physical Origin and Properties (Erice, 1988). Edited by Luciano Pietronero, New York: Plenum, 3-29.

• Short version: Negative fractal dimensions and multifractals. Statistical Physics 17, International IUPAP Conference (Rio de Janeiro, 1989). Edited by Constantino Tsallis, Physica: A163, 1990, 306-315.
[ PDF (3.53 MB) ]
• Updated short version: Two meanings of multifractality, and the notion of negative fractal dimension. Chaos/Xaoc: Soviet-American Perspectives on Nonlinear Science (Woods Hole, 1989). Edited by David K. Campbell. New York: American Institute of Physics, 1990, 79-90.


  124

WWW M. M 1990t. Limit lognormal multifractal measures. Frontiers of Physics: Landau Memorial Conference (Tel Aviv, 1988). Edited by E. A. Gotsman et al. New York: Pergamon, 309-340.


  130

WWW M. M 1991k. Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Proceedings of the Royal Society (London): A434, 79-88. Also in Turbulence and Stochastic Processes: Kolmogorov’s ideas 50 years on. Edited by Julian C. R. Hunt, O. M. Phillips, & D. Williams, London: The Royal Society.
[ PDF (2.92 MB) ]


  150

WWW M. M 1995k. Negative dimensions and Hölder, multifractals and their Hölder spectra, and the role of lateral preasymptotics in science. J. P. Kahane meeting (Paris, 1993). Edited by Aline Bonami & Jacques Peyrière. The Journal of Fourier Analysis and Applications: special issue, 409-432.


  179

WWW M. M 2003f. Multifractal power-law distributions, other “anomalies,” and critical dimensions, explained by a simple example. Journal of Statistical Physics: 110, 739-777.
[ PDF (451 KB) ]


  180

WWW P. M 2003r. Heavy tails in finance for independent or multifractal price increments. Handbook on Heavy Tailed Distributions in Finance. Edited by Svetlozar T. Rachev (Handbooks in Finance: 30, Senior Editor: William T. Ziemba): 1, 1-34.
[ PDF (295.1 KB) ]