Gaussian multiplicative Chaos for symmetric isotropic matrices
Laurent Chevillard (Phys-ENS), R\'emi Rhodes (CEREMADE), Vincent, Vargas (CEREMADE)
TL;DR
This paper develops a theory of symmetric matrix-valued isotropic Gaussian multiplicative chaos, extending Kahane's scalar theory to matrix settings, inspired by turbulence phenomena.
Contribution
It introduces a novel matrix-valued Gaussian multiplicative chaos framework extending previous scalar models.
Findings
Provides a rigorous construction of matrix-valued chaos
Extends scalar theory to symmetric matrices
Lays groundwork for turbulence modeling
Abstract
Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.
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Taxonomy
TopicsRandom Matrices and Applications · Quantum chaos and dynamical systems · Quantum Information and Cryptography