Speaker: Gianni Pagnini, BCAM & IKERBASQUE

BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009, Bilbao, Basque Country – Spain

IKERBASQUE – Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Basque Country, Spain

Time : 16:00 - 17.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom :  A zoom meeitng link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  TBA

Abstract: We study the properties of L´evy flights with index 0 < α < 2 at elapsed times smaller than those required for reaching the diffusive limit, and we focus on the bulk of the walkers’ distribution rather than on its tails. On the basis of the analogs of the Kramers–Moyal expansion and of the Pawula theorem, we show that, for any α ≤ 2/3, the bulk of the walkers’ distribution occurs at wave-numbers greater than (2/α)1/(2) ≥ 1, and it remains non-self-similar for a time-scale longer than the Markovian time-lag of at least one order of magnitude. This result highlights the fact that for Levy flights, the Markovianity time-lag is not the only time-scale of the process and indeed another and longer time-scale controls the transition to the familiar power-law regime in the final diffusive limit. The magnitude of this further time-scale is independent of the index and may compromise the reliability of applications of Levy flights to real world cases related with recurrence and transience as optimal searching, animal foraging, and site fidelity.

The talk is based on References [1, 2].

Biography:

TBA
 

Bibliography