A Gaussian correlation inequality for plurisubharmonic functions

TL;DR

This paper proves a positive correlation inequality for circular-invariant plurisubharmonic functions under complex Gaussian measures, utilizing advanced semigroup techniques.

Contribution

It introduces a new correlation inequality for a class of functions in complex analysis, expanding the understanding of Gaussian measures in complex spaces.

Findings

Established a positive correlation inequality for circular-invariant plurisubharmonic functions.

Utilized Ornstein-Uhlenbeck and Gaussian $ ext{partial}$-Laplacian semigroups in proofs.

Provides tools for further research in complex Gaussian measures and function inequalities.

Abstract

A positive correlation inequality is established for circular-invariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs are the Ornstein-Uhlenbeck semigroup, and another natural semigroup associated to the Gaussian $\partial$-Laplacian.