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SUMMARY:Some Recent Results in the Theory of Free and Confined Levy Flight
 s - A. V. Chechkin\, Institute for Theoretical Physics\, Kharkov\, Ukraine
DTSTART:20070911T130000Z
DTEND:20070911T140000Z
UID:TALK7966@talks.cam.ac.uk
CONTACT:Nick Watkins
DESCRIPTION:The term Levy motion\, or “Levy flights” (LFs) was coined 
 for a family of non-Gaussian random processes whose stationary increments 
 are distributed with the Levy stable probability laws discovered by French
  mathematician Paul Pierre Levy. These laws are of importance due to three
  remarkable properties: (i) as the Gaussian law\, stable laws are attracti
 ve to the distributions of sums of random variables\, thus naturally appea
 r when evolution of the physical (chemical\, biological\, ...) system or t
 he result of an experiment is determined by the sum of random factors (Gen
 eralized Central Limit Theorem)\; (ii) in contrast to the Gaussian law\, t
 he probability density functions (PDFs) of the stable laws possess slowly 
 decaying power-law asymptotics\; thus they naturally serve for the descrip
 tion of fluctuation processes with bursts or large outliers\; and (iii) as
  the Brownian motion\, which increments are distributed with the Gaussian 
 law\, the Levy motions are statistically self-similar\, or self-affine\, t
 hus naturally suited for the description of random fractal processes. In m
 y talk I will review at tutorial level some recent results in the LFs theo
 ry. The properties of LFs are discussed with the use of analytical and num
 erical solutions of space and time fractional kinetic equations as well as
  numerical simulation based on the Langevin approach.
LOCATION:British Antarctic Survey\, Room 330B
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