Gaussian Multiplicative Chaos revisited

Raoul Robert (1) , Vincent Vargas (2)

1 IF - Institut Fourier
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this article, we extend the theory of multiplicative chaos for positive definite functions in Rd of the form f(x) = 2 ln+ T|x|+ g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main application, we give a rigorous mathematical meaning to the Kolmogorov-Obukhov model of energy dissipation in a turbulent flow.

Mots clés: Random measures; Gaussian processes; Multifractal processes

Domaines: Probabilités [math.PR]

Raoul Robert, Vincent Vargas. Gaussian Multiplicative Chaos revisited. 2008. ⟨hal-00293830⟩