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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Infinite densities for Lévy walks

## Infinite densities for Lévy walksAdd to your list(s) Download to your calendar using vCal - Eli Barkai (Bar-Ilan University)
- Thursday 24 March 2022, 09:00-09:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. FD2W02 - Fractional kinetics, hydrodynamic limits and fractals In many cases anomalous diffusion processesexhibit a bi-fractal property. For example active transport in the cell breaks the basic concepts of scaling.In the presence of ATP , $q>0$ moments of the tracer particle displacement$\langle |x|^q \rangle$, increase eithersuper-diffusively or quasi ballistically for values of $q$ below or abovea critical value $q_c$ respectively. This dual nature of the transport isfound in many systems including deterministic modelslike the Lorentz gas [1] and stochastic approaches like the L\’evy walk. Given thatstandard fractional diffusion equationsfail to describe this widely observed bi-scalingwe investigate the problem using the widely applicable L\’evy walk model. We showthat non-normalised infinite densities are complementary to the standard L’evy-Gauss central limittheorems in the statistical description of the process [2.3]. [1] Lior Zarfaty,Alexander Peletskyi,EB, andSergey DenisovInfinite horizon billiards: Transport at the border between Gauss and L\’evy universality classes, Phys. Rev. E. 100, 042140 (2019). [2] A. Rebenshtok, S. Denisov, P. H\”anggi, and E. Barkai,Non-normalizable densities in strong anomalous diffusion: beyondthe central limit theorem, Phys. Rev. Letters, 112, 110601 (2014). [3] A. Rebenshtok, S. Denisov, P. H\”anggi, and E. Barkai, Infinite densities for L\’evy walks Phys. Rev. E.90, 062135 (2014). This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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