Ergodic properties of random holomorphic endomorphisms of $\Bbb{P}^k$

Abstract

We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which have good invariance and convergence properties. We provide a sufficient condition for these currents to have Hölder continuous quasi-potentials. We also prove central limit theorem for d.s.h and Hölder continuous observables.