Exponential estimates for plurisubharmonic functions and stochastic dynamics

TL;DR

This paper establishes exponential estimates for plurisubharmonic functions related to Monge-Ampere measures and applies these results to demonstrate stochastic properties like decay of correlations, CLT, and large deviations for equilibrium measures in holomorphic dynamics.

Contribution

It introduces exponential estimates for plurisubharmonic functions with Holder continuous potentials and applies them to derive stochastic properties of equilibrium measures in complex dynamics.

Findings

Exponential decay of correlations for equilibrium measures

Central limit theorem for d.s.h. observables

Large deviations principle for bounded and Holder continuous observables

Abstract

We prove exponential estimates for plurisubharmonic functions with respect to Monge-Ampere measures with Holder continuous potential. As an application, we obtain several stochastic properties for the equilibrium measures associated to holomorphic maps on projective spaces. More precisely, we prove the exponential decay of correlations, the central limit theorem for general d.s.h. observables, and the large deviations theorem for bounded d.s.h. observables and Holder continuous observables.