The Annals of Probability

Gaussian multiplicative chaos revisited

Raoul Robert and Vincent Vargas

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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.

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Ann. Probab., Volume 38, Number 2 (2010), 605-631.

First available in Project Euclid: 9 March 2010

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Zentralblatt MATH identifier

Primary: 60G57: Random measures 60G15: Gaussian processes 60G25: Prediction theory [See also 62M20] 28A80: Fractals [See also 37Fxx]

Random measures Gaussian processes multifractal processes


Robert, Raoul; Vargas, Vincent. Gaussian multiplicative chaos revisited. Ann. Probab. 38 (2010), no. 2, 605--631. doi:10.1214/09-AOP490.

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