Gaussian multiplicative Chaos for symmetric isotropic matrices

Laurent Chevillard (1) , Rémi Rhodes (2) , Vincent Vargas (2)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Gaussian multiplicative chaos; random matrices; noncommutativity

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

Laurent Chevillard, Rémi Rhodes, Vincent Vargas. Gaussian multiplicative Chaos for symmetric isotropic matrices. Journal of Mathematical Physics, 2013, 150 (4). ⟨hal-00714919v2⟩