Gaussian multiplicative chaos revisited

Abstract

In this article, we extend the theory of multiplicative chaos for positive definite functions in ℝd of the form f(x)=λ2ln+ R/|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 [Ann. Sci. Math. Québec 9 (1985) 105–150]. As a main application, we provide a rigorous mathematical meaning to the Kolmogorov–Obukhov model of energy dissipation in a turbulent flow.