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

Kamil Kaleta, József Lőrinczi

Published 2015-07-07Version 1

The time evolution of random variables with L\'evy statistics has the ability to develop jumps displaying very different behaviours from continuously fluctuating cases. Such patterns appear in an ever broadening range of sources 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 behaviour 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 in the fundamental question of what is the mechanism of the spatial decay of a ground state.