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We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [1]. If M is a non degenerate multifractal measure with associated metric ρ(x, y) = M ([x, y]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dim H of a measurable set K and the(More)
This paper deals with homogenization of diffusion processes in a locally stationary random environment. Roughly speaking, such an environment possesses two evolution scales: both a fast microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims at giving a macro-scopic approximation that takes into account the microscopic(More)
We investigate stochastic homogenization for some degenerate quasilinear pa-rabolic PDEs. The underlying nonlinear operator degenerates along the space variable, uniformly in the nonlinear term: the degeneracy points correspond to the degeneracy points of a reference diffusion operator on the random medium. Assuming that this reference diffusion operator is(More)
Gaussian Multiplicative Chaos is a way to produce a measure on R d (or subdo-main of R d) of the form e γX(x) dx, where X is a log-correlated Gaussian field and γ ∈ [0, √ 2d) is a fixed constant. A renormalization procedure is needed to make this precise, since X oscillates between −∞ and ∞ and is not a function in the usual sense. This procedure yields the(More)