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

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.

A flaw in the proof of Theorem 3.1 is corrected

References in corpus (2)

• Value distribution for sequences of rational mappings and complex dynamics
• Endomorphismes aleatoires dans les espaces projectifs II

Cited by in corpus (2)

• Dynamical height growth: left, right, and total orbits
• Almost Sure Invariance Principle for non-autonomous holomorphic dynamics in ${\mathbb{P}}^k$