Rémi Rhodes

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The purpose of this paper is to introduce a natural multidimensional generalization (MMRM) of the one dimensional multifractal random measures (MRM) introduced by Bacry and Muzy in [1]. The measures M we introduce are different from zero, homogeneous in space, isotropic and satisfy the following exact scale invariance relation: if T denotes some given(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 macroscopic approximation that takes into account the microscopic(More)
This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomic random measures corresponding to values of the parameter γ2 beyond the transition phase (i.e. γ2 > 2d) and check the duality relation with sub-critical Gaussian multiplicative(More)
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that(More)