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