Lévy Flights and Related Topics in Physics

Variability of anomalous transport exponents versus different physical situations in geophysical and laboratory turbulence.- Conditionally-averaged dynamics of turbulence, new scaling and stochastic modelling.- Observation of anomalous diffusion and Lévy flights.- Chaotic lagrangian motion on a rotating sphere.- Lévy walks and lattice gas hydrodynamics.- Definition of stable laws, infinitely divisible laws, and Lévy processes.- to fractal sums of pulses.- Time scales in noisy conservative systems.- Geometric constructions in multifractality formalism.- Lévy walks in chaotic systems: Useful formulas and recent applications.- Transport and large scale stochasticity for a nonperiodic generalisation of the standard map.- Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states.- Lévy description of anomalous diffusion in dynamical systems.- From Lévy flights to the fractional kinetic equation for dynamical chaos.- More Lévy distributions in physics.- Aspects of Lévy flights in a quenched random force field.- Universality of escape from a half-space for symmetrical random walks.- Derivation of Lévy-type anomalous superdiffusion from generalized statistical mechanics.- A dynamical model leading to the breakdown of the Green-Kubo predictions.- Ultra-slow convergence to a Gaussian: The truncated Lévy flight.- Fractals in physiological control: From heart beat to gait.- Long-range correlations and generalized Lévy walks in DNA sequences.

P. Lévy's work on random walks with infinite moments is 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 is introduced by B. Mandelbrot.