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

Abstract

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.

References in corpus (5)

• The scaling laws of human travel
• Lévy walks
• On distributions of functionals of anomalous diffusion paths
• Multi-point Distribution Function for the Continuous Time Random Walk
• Exponential increase of transition rates in metastable systems driven by non-Gaussian noise

Cited by in corpus (8)

• Fractional Laplacians in bounded domains: Killed, reflected, censored and taboo Lévy flights
• Killing (absorption) versus survival in random motion
• Multifractal properties of sample paths of ground state-transformed jump processes
• Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
• Levy flights in steep potential wells: Langevin modeling versus direct response to energy landscapes
• Ultrarelativistic bound states in the shallow spherical well
• Fractional Laplacians and Levy flights in bounded domains
• Special potentials for relativistic Laplacians I: Fractional Rollnik-class