Reconstruction of log-correlated fields from multiplicative chaos measures

2024/08/30 by Sami Vihko, Vihko, Sami
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2408.17219

openalex publication_date 2024/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider log-correlated random fields X and the associated multiplicative chaos measures μ_γ,X. Our results reconstruct the underlying field X from the multiplicative chaos measure ν_γ,X. The new feature of our results is that we allow the dimension d to be arbitrary and cover also the critical case γ=√(2d). In the sub-critical regime γ<√(2d), we allow the fields to be mildly non-Gaussian, that is, the field has the decomposition X=G+H with a log-correlated Gaussian field G and a Hölder-continuos (not necessarily Gaussian) field H.

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