Gaussian Multiplicative Chaos revisited

TL;DR

This paper extends the theory of Gaussian multiplicative chaos to more general functions, simplifying the construction and applying it to model energy dissipation in turbulence.

Contribution

It introduces a more general and simpler construction of multiplicative chaos for certain positive definite functions, broadening the theoretical framework.

Findings

Provides a rigorous mathematical foundation for the Kolmogorov-Obukhov turbulence model

Simplifies the construction of multiplicative chaos compared to Kahane's original approach

Extends the theory to functions of the form f(x) = 2 ln+ T|x|+ g(x)

Abstract

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.