Gaussian multiplicative chaos revisited

By R. Robert, Vincent Vargas. 2008

198 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ebb6e25d12deaf3ee6d0b6bf63142ba8ecafea68

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Citations in the corpus

Uniqueness of critical Gaussian chaos (2017, methodology): “More general results developing the method of [26] are contained in the review [25] due to Rhodes and Vargas, whose conditions are very similar to ours.”
Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions (2014, methodology): “Such bounds have been proven in [23] in the case that the multiplicative chaos is associated with a family of Gaussian fields whose covariance function is contained a certain class of convolution kernels.”
Gaussian multiplicative chaos and applications: A review (2013, methodology): “Here is the main theorem of [132]: Theorem 3.”
An elementary approach to Gaussian multiplicative chaos (2015, background): “Simultaneously, Rhodes and Vargas, [10], among other things, showed that Gaussian multiplicative chaos can be used directly to construct the same object.”
Intermittent process analysis with scattering moments (2013, background): “Indeed, as shown in [34] it is possible to choose the way ωl is regularized at scale l.”
Freezing and Decorated Poisson Point Processes (2014, background): “introduced by Kahane [34], which has recently became the object of renewed interest [2, 44, 45, 46, 47].”
On Gaussian multiplicative chaos (2014, methodology): “Mollifying operators [11, 3, 10] This technique restricts the generality to the case where T is a domain in R, μ is the Lebesgue measure, and the covaraince kernel K (t, s) := EX (t)X (s) has the special form K (t, s) = γ(2) log ‖t− s‖ + g (t, s) , (2) where the function g : T ×T → R is bounded and ”