Decay of correlations and central limit theorem for meromorphic maps

TL;DR

This paper constructs an equilibrium measure for certain meromorphic maps on compact Kaehler manifolds, proves it is exponentially mixing, and establishes a central limit theorem for Lipschitz observables.

Contribution

It introduces a new method for constructing equilibrium measures and proves exponential mixing and CLT for meromorphic maps on Kaehler manifolds.

Findings

Equilibrium measure constructed for meromorphic maps.

Proved exponential mixing of the measure.

Established central limit theorem for Lipschitz observables.

Abstract

Let f be a dominating meromorphic self-map of large topological degree on a compact Kaehler manifold. We give a new construction of the equilibrium measure of f and prove that it is exponentially mixing. Then, we deduce the central limit theorem for Lipschitzian observables.