A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions

TL;DR

This paper extends the Gaussian correlation conjecture to multivariate gamma distributions, providing a proof that broadens the conjecture's applicability beyond Gaussian measures.

Contribution

The paper offers a simple proof extending the Gaussian correlation conjecture to multivariate gamma distributions, generalizing the classical result for Gaussian measures.

Findings

Proved the Gaussian correlation conjecture for multivariate gamma distributions.

Connected the classical Gaussian case as a special instance with one degree of freedom.

Extended the applicability of the Gaussian correlation conjecture to a broader class of distributions.

Abstract

An extension of the Gaussian correlation conjecture (GCC) is proved for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy). The classical GCC for Gaussian probability measures is obtained by the special case with one degree of freedom.