Benoît B. Mandelbrot

Journal Articles

1. Benoît B. Mandelbrot (2014). Fractional Brownian Motions and Fractional Gaussian Noises. Wiley StatsRef: Statistics Reference Online.DOI
2. Benoît B. Mandelbrot (2014). Fractional Integrodifferentiation. Wiley StatsRef: Statistics Reference Online.DOI
3. Julien Barral, Xiong Jin, Benoît B. Mandelbrot (2010). Uniform convergence for complex [0, 1]-martingales. The Annals of Applied Probability.DOI
4. Julien Barral, Benoît B. Mandelbrot (2009). Fractional multiplicative processes. Annales de l Institut Henri Poincaré Probabilités et Statistiques.DOI
5. Benoît B. Mandelbrot, Michael L. Frame (2009). A PRIMER OF NEGATIVE TEST DIMENSIONS AND DEGREES OF EMPTINESS FOR LATENT SETS. Fractals.DOI
6. Benoît B. Mandelbrot (2008). “New Methods of Statistical Economics,” revisited: Short versus long tails and Gaussian versus power‐law distributions. Complexity.DOI
7. Benoît B. Mandelbrot (2006). Benoit Mandelbrot. The New Scientist.DOI
8. Benoît B. Mandelbrot (2006). Fractal Analysis and Synthesis of Fracture Surface Roughness and Related Forms of Complexity and Disorder. International Journal of Fracture.DOI
9. Benoît B. Mandelbrot (2005). The inescapable need for fractal tools in finance. Annals of Finance.DOI
10. Benoît B. Mandelbrot (2005). Parallel cartoons of fractal models of finance. Annals of Finance.DOI
11. Benoît B. Mandelbrot (2004). Fractional B rownian Motions and Fractional G aussian Noises. Encyclopedia of Statistical Sciences.DOI
12. Benoît B. Mandelbrot (2004). Fractional Integrodifferentiation. Encyclopedia of Statistical Sciences.DOI
13. Benoît B. Mandelbrot (2004). SELECTED TOPICS IN MATHEMATICS, PHYSICS, AND FINANCE ORIGINATING IN FRACTAL GEOMETRY.DOI
14. Benoît B. Mandelbrot (2004). Acknowledgments related to quadratic dynamics. Springer eBooks.DOI
15. Benoît B. Mandelbrot (2003). Multifractal Power Law Distributions: Negative and Critical Dimensions and Other “Anomalies,” Explained by a Simple Example. Journal of Statistical Physics.DOI
16. Benoît B. Mandelbrot, Michael L. Frame (2003). Fractals. Elsevier eBooks.DOI
17. Julien Barral, Benoît B. Mandelbrot (2002). Multifractal products of cylindrical pulses. Probability Theory and Related Fields.DOI
18. Benoît B. Mandelbrot, Boaz Kol, Amnon Aharony (2002). Angular Gaps in Radial Diffusion-Limited Aggregation: Two Fractal Dimensions and Nontransient Deviations from Linear Self-Similarity. Physical Review Letters.DOI
19. Benoît B. Mandelbrot (2001). TOPICS ON FRACTALS IN MATHEMATICS AND PHYSICS.DOI
20. Benoît B. Mandelbrot, Michael L. Frame (1999). The Canopy and Shortest Path in a Self-Contacting Fractal Tree. The Mathematical Intelligencer.DOI
21. Benoît B. Mandelbrot (1999). Renormalization and fixed points in finance, since 1962. Physica A Statistical Mechanics and its Applications.DOI
22. Benoît B. Mandelbrot (1998). Is Nature Fractal? Science.DOI
23. Rudolf H. Riedi, Benoît B. Mandelbrot (1998). Exceptions to the multifractal formalism for discontinuous measures. Mathematical Proceedings of the Cambridge Philosophical Society.DOI
24. Laurent E. Calvet, Laurent E. Calvet, A. Fisher, Benoit B. Mandelbrot, Benoit B. Mandelbrot (1997). Large Deviations and the Distribution of Price Changes.
25. Rudolf H. Riedi, Benoît B. Mandelbrot (1997). Inversion Formula for Continuous Multifractals. Advances in Applied Mathematics.DOI
26. Benoît B. Mandelbrot, Stéphane Jaffard (1997). Peano-pólya motions, when time is intrinsic or binomial (uniform or multifractal). The Mathematical Intelligencer.DOI
27. Raphaël Blumenfeld, Benoît B. Mandelbrot (1997). Lévy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.DOI
28. Benoît B. Mandelbrot, Rudolf H. Riedi (1997). Inverse Measures, the Inversion Formula, and Discontinuous Multifractals. Advances in Applied Mathematics.DOI
29. J.-P. Hovi, Amnon Aharony, Dietrich Stauffer, Benoît B. Mandelbrot (1996). Gap Independence and Lacunarity in Percolation Clusters. Physical Review Letters.DOI
30. Stéphane Jaffard, Benoît B. Mandelbrot (1996). Local Regularity of Nonsmooth Wavelet Expansions and Application to the Polya Function. Advances in Mathematics.DOI
31. Henry Kaufman, Alessandro Vespignani, Benoît B. Mandelbrot, Lionel J. Woog (1995). Parallel diffusion-limited aggregation. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.DOI
32. M. Atiyah, A. Borel, G. Chaitin, Daniel Friedan, J. Glimm, Jeremy J. Gray, M. Hirsch, S. Maclane, Benoit B. Mandelbrot, D. Ruelle, Albert Schwarz, Karen Uhlenbeck, R. Thom, Edward Witten, Christopher Zeeman (1994). Responses to ``Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn.
33. Benoît B. Mandelbrot (1993). OPINIONS. Fractals.DOI
34. Benoît B. Mandelbrot (1992). Plane DLA is not self-similar; is it a fractal that becomes increasingly compact as it grows? Physica A Statistical Mechanics and its Applications.DOI
35. Carl J. G. Evertsz, Benoît B. Mandelbrot (1992). Self-similarity of harmonic measure on DLA. Physica A Statistical Mechanics and its Applications.DOI
36. Carl J. G. Evertsz, Benoît B. Mandelbrot, Lionel J. Woog (1992). Variability of the form and of the harmonic measure for small off-off-lattice diffusion-limited aggregates. Physical Review A.DOI
37. Benoît B. Mandelbrot, Carl J. G. Evertsz (1991). Multifractality of the harmonic measure on fractal aggregates, and extended self-similarity. Physica A Statistical Mechanics and its Applications.DOI
38. Carl J. G. Evertsz, Benoît B. Mandelbrot (1991). Fractal aggregates, and the current lines of their electrostatic potentials. Physica A Statistical Mechanics and its Applications.DOI
39. Benoît B. Mandelbrot (1991). Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences.DOI
40. Benoît B. Mandelbrot, Carl J. G. Evertsz (1990). The potential distribution around growing fractal clusters. Nature.DOI
41. Benoît B. Mandelbrot, Carl J. G. Evertsz, Yoshinori Hayakawa (1990). Exactly self-similar left-sided multifractal measures. Physical Review A.DOI
42. Benoît B. Mandelbrot (1990). New “anomalous” multiplicative multifractals: Left sided ƒ(α) and the modelling of DLA. Physica A Statistical Mechanics and its Applications.DOI
43. Benoît B. Mandelbrot (1990). Negative fractal dimensions and multifractals. Physica A Statistical Mechanics and its Applications.DOI
44. Benoît B. Mandelbrot (1989). Some “Facts” That Evaporate Upon Examination. The Mathematical Intelligencer.DOI
45. Benoît B. Mandelbrot (1989). Fractal geometry: what is it, and what does it do? Proceedings of the Royal Society of London A Mathematical and Physical Sciences.DOI
46. Benoît B. Mandelbrot (1989). Multifractal measures, especially for the geophysicist. Pure and Applied Geophysics.DOI
47. Benoît B. Mandelbrot, James R. Wallis (1969). Some long‐run properties of geophysical records. Water Resources Research.DOI

Preprints

1. Benoît B. Mandelbrot, Adlai J. Fisher, Laurent E. Calvet (2011). A Multifractal Model of Asset Returns. RePEc: Research Papers in Economics.
2. Adlai J. Fisher, Laurent E. Calvet, Benoît B. Mandelbrot (1997). Multifractality of Deutschemark/US Dollar Exchange Rates. RePEc: Research Papers in Economics.

Book Chapters

1. Benoît B. Mandelbrot (2008). Introduction to fractal sums of pulses. Springer eBooks.DOI
2. Benoît B. Mandelbrot (2007). Fractal analysis and synthesis of fracture surface roughness and related forms of complexity and disorder. Springer eBooks.DOI
3. Benoît B. Mandelbrot (2004). Fractal aspects of the iteration of z→λz(1-z) for complex λ and z. Springer eBooks.DOI
4. Benoît B. Mandelbrot (2004). Self-inverse fractals, Apollonian nets, and soap. Springer eBooks.DOI
5. Benoît B. Mandelbrot (2004). Introduction to papers on quadratic dynamics: a progression from seeing to discovering. Springer eBooks.DOI
6. Benoît B. Mandelbrot (2004). The boundary of the ℳ-set is of dimension 2. Springer eBooks.DOI
7. Benoît B. Mandelbrot (2004). Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski. Springer eBooks.DOI
8. Benoît B. Mandelbrot (2004). Symmetry with respect to several circles: dilation/reduction, fractals, and roughness. Springer eBooks.DOI
9. Benoît B. Mandelbrot (2004). Invariant multifractal measures in chaotic Hamiltonian systems and related structures (Gutzwiller & M 1988). Springer eBooks.DOI
10. Benoît B. Mandelbrot (2004). Certain Julia sets include smooth components. Springer eBooks.DOI
11. Benoît B. Mandelbrot (2004). The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai). Springer eBooks.DOI
12. Benoît B. Mandelbrot (2004). The complex quadratic map and its ℳ-set. Springer eBooks.DOI
13. Benoît B. Mandelbrot (2004). Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991). Springer eBooks.DOI
14. Benoît B. Mandelbrot (2004). Two nonquadratic rational maps devised from Weierstrass doubling formulas. Springer eBooks.DOI
15. Benoît B. Mandelbrot (2004). The inexhaustible function z squared plus c. Springer eBooks.DOI
16. Benoît B. Mandelbrot (2004). Self-inverse fractals osculated by sigma-discs: the limit sets of (“Kleinian”) inversion groups. Springer eBooks.DOI
17. Benoît B. Mandelbrot (2004). Bifurcation points and the “n-squared” approximation and conjecture, illustrated by M.L Frame and K Mitchell. Springer eBooks.DOI
18. Benoît B. Mandelbrot (2004). The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems. Springer eBooks.DOI
19. Benoît B. Mandelbrot (2004). Mathematical analysis while in the wilderness. Springer eBooks.DOI
20. Benoît B. Mandelbrot (2004). The “normalized radical” of the ℳ-set. Springer eBooks.DOI
21. Benoît B. Mandelbrot (2004). Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets. Springer eBooks.DOI
22. Benoît B. Mandelbrot (2004). Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas. Springer eBooks.DOI
23. Benoît B. Mandelbrot (2004). The Fatou and Julia stories. Springer eBooks.DOI
24. Benoît B. Mandelbrot (2004). Cantor and Fatou dusts; self-squared dragons. Springer eBooks.DOI
25. Benoît B. Mandelbrot (2004). Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments. Springer eBooks.DOI
26. Benoît B. Mandelbrot (2004). Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs. Springer eBooks.DOI
27. Benoît B. Mandelbrot (2003). Heavy Tails in Finance for Independent or Multifractal Price Increments. Elsevier eBooks.DOI
28. Benoît B. Mandelbrot (2003). Fractal Sums of Pulses and a Practical Challenge to the Distinction Between Local and Global Dependence. Lecture notes in physics.DOI
29. Benoît B. Mandelbrot (2003). Fractais. Imprensa da Universidade de Coimbra eBooks.DOI
30. Benoît B. Mandelbrot (1999). Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Springer eBooks.DOI
31. Benoît B. Mandelbrot (1999). Intermittent turbulence and fractal dimension: kurtosis and the spectral exponent 5/3 + B. Springer eBooks.DOI
32. Benoît B. Mandelbrot (1999). Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence. Springer eBooks.DOI
33. Benoît B. Mandelbrot (1999). Iterated random multiplications and invariance under randomly weighted averaging. Springer eBooks.DOI
34. Benoît B. Mandelbrot (1999). Intermittent free turbulence. Springer eBooks.DOI
35. Benoît B. Mandelbrot (1999). Sporadic random functions and conditional spectra; self-similar examples and limits. Springer eBooks.DOI
36. Benoît B. Mandelbrot (1999). Filtering and specification of self-affinity. Springer eBooks.DOI
37. Benoît B. Mandelbrot (1999). Co-indicator functions and related 1/ƒ noises. Springer eBooks.DOI
38. Marc‐Olivier Coppens, Benoît B. Mandelbrot (1999). Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions. Fractals.DOI
39. Benoît B. Mandelbrot (1999). Self-similarity and conditional stationarity. Springer eBooks.DOI
40. Benoît B. Mandelbrot (1999). Fractal dimension, dispersion, and singularities of fluid motion. Springer eBooks.DOI
41. Benoît B. Mandelbrot (1999). “On certain martingales of Benoit Mandelbrot” Guest contribution (Kahane & Peyrière 1976). Springer eBooks.DOI
42. Benoît B. Mandelbrot (1999). Random sets of multiplicity for trigonometric series (Kahane & M 1965). Springer eBooks.DOI
43. Benoît B. Mandelbrot (1999). New model for the clustering of errors on telephone circuits (Berger & M 1963). Springer eBooks.DOI
44. Benoît B. Mandelbrot (1999). Panorama of grid-bound self-affine variability. Springer eBooks.DOI
45. Benoît B. Mandelbrot (1999). Sketches of prehistory and history. Springer eBooks.DOI
46. Benoît B. Mandelbrot (1999). Sporadic turbulence. Springer eBooks.DOI
47. Benoît B. Mandelbrot (1999). 1/ƒ noises and the infrared catastrophe. Springer eBooks.DOI
48. Benoît B. Mandelbrot (1999). Scaling, invariants and fixed points. Springer eBooks.DOI
49. Benoît B. Mandelbrot (1999). Short excerpts (1964–1984). Springer eBooks.DOI
50. Benoît B. Mandelbrot (1997). The variation of certain speculative prices. Springer eBooks.DOI
51. Benoît B. Mandelbrot (1997). New methods in statistical economics. Springer eBooks.DOI
52. Benoît B. Mandelbrot (1997). The variation of the prices of cotton, wheat, and railroad stocks, and of some financial rates. Springer eBooks.DOI
53. Benoît B. Mandelbrot (1997). Nonlinear forecasts, rational bubbles, and martingales. Springer eBooks.DOI
54. Benoît B. Mandelbrot (1997). Mandelbrot on price variation. Springer eBooks.DOI
55. Benoît B. Mandelbrot (1997). States of randomness from mild to wild, and concentration from the short to the long run. Springer eBooks.DOI
56. Benoît B. Mandelbrot (1997). A case against the lognormal distribution. Springer eBooks.DOI
57. Benoît B. Mandelbrot (1997). Industrial concentration and scaling. Springer eBooks.DOI
58. Benoît B. Mandelbrot (1997). Limitations of efficiency and of martingale models. Springer eBooks.DOI
59. Benoît B. Mandelbrot (1997). Discontinuity and scaling: their scope and likely limitations. Springer eBooks.DOI
60. Benoît B. Mandelbrot (1997). Comments by P. H. Cootner, E. Parzen, and W. S. Morris (1960s) and responses. Springer eBooks.DOI
61. Benoît B. Mandelbrot (1997). Self-similarity and panorama of self-affinity. Springer eBooks.DOI
62. Benoît B. Mandelbrot (1997). Rank-size plots, Zipf’s law, and scaling. Springer eBooks.DOI
63. Benoît B. Mandelbrot (1997). Scaling distributions and income maximization. Springer eBooks.DOI
64. Benoît B. Mandelbrot (1997). L-stable model for the distribution of income. Springer eBooks.DOI
65. Benoît B. Mandelbrot (1997). Computation of the L-stable distributions. Springer eBooks.DOI
66. Benoît B. Mandelbrot (1997). Sources of inspiration and historical background. Springer eBooks.DOI
67. Benoît B. Mandelbrot (1997). Proportional growth with or without diffusion, and other explanations of scaling. Springer eBooks.DOI
68. Benoît B. Mandelbrot (1997). Introduction. Springer eBooks.DOI
69. Benoît B. Mandelbrot (1997). L-stability and multiplicative variation of income. Springer eBooks.DOI
70. Benoît B. Mandelbrot (1995). Measures of Fractal Lacunarity: Minkowski Content and Alternatives. Birkhäuser Basel eBooks.DOI
71. Benoît B. Mandelbrot (1995). The Statistics of Natural Resources and the Law of Pareto. Springer eBooks.DOI
72. Benoît B. Mandelbrot (1994). A Fractal’s Lacunarity, and how it can be Tuned and Measured. Birkhäuser Basel eBooks.DOI
73. Benoît B. Mandelbrot (1989). Multifractal Measures, Especially for the Geophysicist. Birkhäuser Basel eBooks.DOI
74. Benoît B. Mandelbrot (1989). A Class of Multinomial Multifractal Measures with Negative (Latent) Values for the “Dimension” f(α). Springer eBooks.DOI

Books

1. Benoît B. Mandelbrot (2004). Fractals and Chaos. Springer eBooks.DOI
2. Benoît B. Mandelbrot (1999). Multifractals and 1/ƒ Noise. Springer eBooks.DOI
3. Benoît B. Mandelbrot (1997). Fractals and Scaling in Finance. Springer eBooks.DOI