Inferring Lévy walks from curved trajectories: A rescaling method

Area of Science:

• Physics
• Complex Systems
• Statistical Mechanics

Background:

• Analyzing anomalous diffusion and transport relies on accurate trajectory data analysis.
• Inferring Lévy walk patterns in 2D and 3D is challenging due to path curvature, unlike in 1D.

Purpose of the Study:

• To evaluate a 1D projection method for detecting 2D Lévy walks with curvature.
• To differentiate between Lévy walks and Markovian correlated random walks with identical step and angle distributions.

Main Methods:

• Applied a 1D projection method to 2D and 3D trajectory data.
• Introduced data rescaling and coarse-graining to the projection method.
• Analyzed the probability density function (pdf) of travel distances for fat-tailed signatures.

Main Results:

• The rescaled projection method reveals a fat tail in the pdf for Lévy walks, distinguishing them from correlated random walks.
• This method effectively identifies Lévy walks even in the presence of noise from path curvature.
• Correlated random walks do not exhibit the fat-tailed signature under the same analysis.

Conclusions:

• The enhanced projection method reliably detects Lévy walks in complex, curved trajectories.
• This protocol offers a valuable tool for analyzing animal movement and other real-world transport phenomena.
• The findings contribute to ongoing debates about Lévy walk prevalence in natural systems.