Transition_rev.pdf (116.1 kB)
Download file

Transition in the decay rates of stationary distributions of Levy motion in an energy landscape

Download (116.1 kB)
journal contribution
posted on 2015-09-08, 12:12 authored by Kamil Kaleta, Jozsef Lorinczi
The time evolution of random variables with Lévy statistics has the ability to develop jumps, displaying very different behaviors from continuously fluctuating cases. Such patterns appear in an ever broadening range of examples including random lasers, non-Gaussian kinetics, or foraging strategies. The penalizing or reinforcing effect of the environment, however, has been little explored so far. We report a new phenomenon which manifests as a qualitative transition in the spatial decay behavior of the stationary measure of a jump process under an external potential, occurring on a combined change in the characteristics of the process and the lowest eigenvalue resulting from the effect of the potential. This also provides insight into the fundamental question of what is the mechanism of the spatial decay of a ground state.



  • Science


  • Mathematical Sciences

Published in

Physical Review E




KALETA, K. and LORINCZI, J., 2016. Transition in the decay rates of stationary distributions of Lévy motion in an energy landscape. Physical Review E, 93, 022135.


© American Physical Society


AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at:

Publication date



This article was published in Physical Review E [© American Physical Society] and the definitive version is available at:



Article number