Superdiffusive dispersals impart the geometry of underlying random walks

TL;DR

This paper demonstrates that the geometry of planar superdiffusive Le9vy walks can be inferred from the asymptotic distribution of walkers, revealing underlying microscopic structures through trajectory analysis.

Contribution

It introduces a method to deduce the geometry of superdiffusive Le9vy walks from trajectory data using an analogue of the Pearson coefficient.

Findings

The asymptotic distribution encodes the walk's geometry.

A Pearson coefficient analogue can infer underlying walk structures.

Planar superdiffusive walks differ from standard random walks in geometric imprinting.

Abstract

It is recognised now that a variety of real-life phenomena ranging from diffuson of cold atoms to motion of humans exhibit dispersal faster than normal diffusion. L\'evy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive L\'evy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.