2023/10/03 by Samy Lakhal, Lakhal, Samy, Laurent Ponson +5 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Data Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2310.01927
openalex publication_date 2023/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a powerful yet simple method that generates multifractal fields with fully controlled scaling properties. Adopting the Multifractal Random Walk (MRW) model of Bacry et al. (2001), synthetic multifractal fields are obtained from the fractional integration of non-Gaussian fluctuations, built by a non-linear transformation of log-correlated Gaussian fields. The resulting fields are parameterized by their roughness exponent H, intermittency λ and multifractal range ξω. We retrieve all the salient features of the MRW, namely a quadratic scaling exponent spectrum ζq, fat-tail statistics of fluctuations, and spatial correlations of local volatility. Such features can be finely tuned, allowing for the generation of ideal multifractals mimicking real multi-affine fields. The construction procedure is then used the other way around to unwrap experimental data -- here the roughness map of a fractured metallic alloy. Our analysis evidences subtle differences with synthetic fields, namely anisotropic filamental clusters reminiscent of dissipation structures found in fluid turbulence.