Lévy Flights and Related Topics in Physics: Proceedings of the International Workshop Held at Nice, France, 27–30 June 1994

A. Tsinober (auth.), Michael F. Shlesinger, George M. Zaslavsky, Uriel Frisch (eds.)3540592229, 9783540592228

P. Lévy’s work on random walks with infinite moments, developed more than half a century ago, has now been fully appreciated as a foundation of probabilistic aspects of fractals and chaos as well as scale-invariant processes. This is the first book for physicists devoted to Lévy processes. It includes thorough review articles on applications in fluid and gas dynamics, in dynamical systems including anomalous diffusion and in statistical mechanics. Various articles approach mathematical problems and finally the volume addresses problems in theoretical biology. The book is introduced by a personal recollection of P. Lévy written by B. Mandelbrot.

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Table of contents :
Variability of anomalous transport exponents versus different physical situations in geophysical and laboratory turbulence….Pages 1-33
Conditionally-averaged dynamics of turbulence, new scaling and stochastic modelling….Pages 35-50
Observation of anomalous diffusion and Lévy flights….Pages 51-71
Chaotic lagrangian motion on a rotating sphere….Pages 72-87
Lévy walks and lattice gas hydrodynamics….Pages 88-95
Definition of stable laws, infinitely divisible laws, and Lévy processes….Pages 97-109
Introduction to fractal sums of pulses….Pages 110-123
Time scales in noisy conservative systems….Pages 124-139
Geometric constructions in multifractality formalism….Pages 140-149
Lévy walks in chaotic systems: Useful formulas and recent applications….Pages 151-173
Transport and large scale stochasticity for a nonperiodic generalisation of the standard map….Pages 174-181
Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states….Pages 182-195
Lévy description of anomalous diffusion in dynamical systems….Pages 196-215
From Lévy flights to the fractional kinetic equation for dynamical chaos….Pages 216-236
More Lévy distributions in physics….Pages 237-250
Aspects of Lévy flights in a quenched random force field….Pages 251-261
Universality of escape from a half-space for symmetrical random walks….Pages 262-268
Derivation of Lévy-type anomalous superdiffusion from generalized statistical mechanics….Pages 269-289
A dynamical model leading to the breakdown of the Green-Kubo predictions….Pages 290-299
Ultra-slow convergence to a Gaussian: The truncated Lévy flight….Pages 300-312
Fractals in physiological control: From heart beat to gait….Pages 313-330
Long-range correlations and generalized Lévy walks in DNA sequences….Pages 331-347