Exponential estimates for plurisubharmonic functions and stochastic dynamics

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.

24 pages, theorem and references added

References in corpus (1)

• Bernoulli coding map and almost sure invariance principle for endomorphisms of ${\mathbb{P}}^k$

Cited by in corpus (15)

• Hölder continuous solutions to Monge-Ampère equations
• Lectures on Stability and Constant Scalar Curvature
• Hölder continuous solutions to complex Hessian equations
• Super-potentials for currents on compact Kaehler manifolds and dynamics of automorphisms
• Universality results for zeros of random holomorphic sections
• On the Moser-Trudinger inequality in complex space
• Complex Monge-Ampère equation for measures supported on real submanifolds
• Continuous solutions to Monge-Ampère equations on Hermitian manifolds for measures dominated by capacity
• Endomorphismes aleatoires dans les espaces projectifs II
• Exponential mixing property for Hénon-Sibony maps of ${\mathbb{C}}^k$
• Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds
• Almost Sure Invariance Principle for non-autonomous holomorphic dynamics in ${\mathbb{P}}^k$
• Monge-Ampere measures on subvarieties
• Equidistribution speed for endomorphisms of projective spaces
• Equidistribution of varieties for endomorphisms of projective spaces