Starts 28 Nov 2017 12:00
Ends 28 Nov 2017 13:00
Central European Time
ICTP
Leonardo Building - Luigi Stasi Seminar Room
In Lévy flights and Lévy walks, large deviations play a crucial role in determining the superdiffusive character of the motion. Indeed, for identically distributed random variables with fat tails, the importance of rare events has been evidenced in the context of Single big jump principle [1] or in physical literature in terms of probability condensation [2]. In Lévy walks far tails of the distribution have been described in details in [3] within the theory of infinite densities, here we will show that the same results can be obtained considering an approach based on the single big jump principle. Lévy flights and walks are typical examples of uncorrelated renewal processes, physical systems however are usually characterized by correlations. In the field of Lévy walks, a typical example is given by the Lévy Lorentz gas model [4] which describes the motion in a Lévy correlated random environment. Here, the superdiffusive properties are crucially determined by topological correlations [5].
I will show that a generalization of the Single big jump principle, which takes into account of the correlation, can be applied to the Lévy Lorentz gas. Also in this case, far tails are are analytically described in terms of an infinite density.
Finally, I will discuss the application of the single, long jump to different models: a model for the Sysufus cooling in cold atoms and a model of Lévy walks with memory. These results evidence that the single long jump principle is a very effective tools which can be applied in a wide class of models.

[1] S. Foss, D. Korshunov and S. Zachary: "An introduction to heavy tailed and supexponential distributions", Springer (2013)
[2] S. N. Majumdar, M. R. Evans and R. K. P. Zia, Phys. Rev. Lett. 94 180601 (2005) [3] A. Rebenshtok, S. Denisov, P. Hanggi and E. Barkai, Phys. Rev. Lett. 112, 110601 (2014)
[4] E. Barkai, V. Fleurov, J. Klafter, Phys. Rev. E 61, 1164 (2000) [5] R. Burioni, L. Caniparoli and A. Vezzani, Phys. Rev. E 81, 060101(R) (2010)