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SUMMARY:Infinite  densities for Lévy walks - Eli Barkai (Bar-Ilan Univers
 ity)
DTSTART:20220324T090000Z
DTEND:20220324T093000Z
UID:TALK171704@talks.cam.ac.uk
DESCRIPTION:In many cases anomalous diffusion processesexhibit a bi-fracta
 l property.&nbsp\;For example &nbsp\;active transport in the cell breaks t
 he basic concepts of scaling.In the presence of ATP\, $q>0$ moments of the
  tracer particle displacement$\\langle |x|^q \\rangle$\, increase eithersu
 per-diffusively or quasi &nbsp\;ballistically for values of $q$ below or a
 bovea critical value $q_c$ respectively. This dual nature of the transport
  isfound in &nbsp\;many systems including deterministic modelslike &nbsp\;
 the Lorentz gas [1]&nbsp\; and stochastic approaches like the L\\'evy walk
 . Given thatstandard fractional &nbsp\;diffusion equationsfail to describe
  this widely observed &nbsp\;bi-scalingwe investigate the problem using th
 e widely applicable L\\'evy walk model. &nbsp\;We showthat non-normalised 
 infinite densities are complementary to the standard L'evy-Gauss &nbsp\;ce
 ntral limittheorems in the statistical description of the process [2.3].\n
 [1] Lior Zarfaty\,Alexander Peletskyi\,EB\, andSergey DenisovInfinite hori
 zon billiards: Transport at the border between Gauss and L\\'evy universal
 ity classes\,&nbsp\;Phys. Rev. E.&nbsp\;100\, 042140 (2019).\n&nbsp\;\n[2]
  A. Rebenshtok\, S. Denisov\, P. H\\"anggi\, and E. Barkai\,Non-normalizab
 le densities in strong anomalous diffusion: beyondthe central limit theore
 m\,&nbsp\;Phys. Rev. Letters\, 112\, 110601 (2014).\n&nbsp\;[3] A. Rebensh
 tok\, S. Denisov\, P. H\\"anggi\, and E. Barkai\,&nbsp\;Infinite densities
  for L\\'evy walks&nbsp\;Phys. Rev. E.90\, 062135 (2014).\n&nbsp\;\n&nbsp\
 ;
LOCATION:Seminar Room 1\, Newton Institute
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