We consider iterated function systems consisting of contracting similarities on the complex plane and prove that for almost every choice of the contraction parameters in the super-critical region (i.e. with similarity dimension greater than 2) the corresponding self-similar measure is absolutely continuous. This extends results of Shmerkin-Solomyak (in the homogenous case) and Saglietti-Shmerkin-Solomyak (in the one-dimensional non-homogeneous case). As the main steps of the proof, we obtain results on the dimension and power Fourier decay of random self-similar measures on the plane, which may be of independent interest. This is joint work with Boris Solomyak.
Meeting ID: 852 4277 3200 Passcode: 103121