Gaussian multiplicative chaos revisited

Raoul Robert; Vincent Vargas

doi:10.1214/09-AOP490

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Home > Journals > Ann. Probab. > Volume 38 > Issue 2 > Article

March 2010 Gaussian multiplicative chaos revisited

Raoul Robert, Vincent Vargas

Ann. Probab. 38(2): 605-631 (March 2010). DOI: 10.1214/09-AOP490

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Abstract

In this article, we extend the theory of multiplicative chaos for positive definite functions in ℝ^d 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.