Should I stay or should I go? Zero-size jumps in random walks for L\'evy flights
Statistical Mechanics
2021-03-15 v1 Probability
Abstract
We study Markovian continuous-time random walk models for L\'evy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in zero. The significance of this result is two-fold: i) with regard to the probabilistic derivation of the fractional diffusion equation and also ii) with regard to the concept of site fidelity in the framework of L\'evy-like motion for wild animals.
Keywords
Cite
@article{arxiv.2103.06981,
title = {Should I stay or should I go? Zero-size jumps in random walks for L\'evy flights},
author = {Gianni Pagnini and Silvia Vitali},
journal= {arXiv preprint arXiv:2103.06981},
year = {2021}
}