Résumé en anglais

In this talk, we will prove the KPZ equation (initially introduced in the framework of quantum gravity in 2 dimensions) for a class of multifractal log infinitely divisible measures (defined in all dimensions). More specifically, for a given set K, we will relate it's Hausdorff dimension under the Euclidian metric to it's Hausdorff dimension under the random metric induced by the multifractal measure. We will see how the notion of stochastic scale invariance is crucial in the proof of the aforementioned relation.