The Levy diffusion as an effect of sporadic randomness

TL;DR

This paper explores Levy diffusion processes, emphasizing their basis in Markovian dynamics with sporadic randomness and the importance of memory erasure in their derivation.

Contribution

It provides a dynamic derivation of Levy diffusion processes highlighting the role of sporadic randomness and memory erasure within a Markovian framework.

Findings

Levy diffusion can be derived from Markov processes with sporadic randomness.

Memory erasure is crucial for the proper theoretical treatment of Levy diffusion.

The process relies on a source of randomness in microscopic dynamics.

Abstract

The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is present in the corresponding microscopic dynamics and (ii) that the consequent process of memory erasure is properly taken into account by the theoretical treatment.