On a Correlation Inequality for Cauchy Type Measures

TL;DR

This paper introduces a new correlation inequality for Cauchy type measures by transforming the problem onto a Riemannian sphere, opening avenues for further research in correlation inequalities.

Contribution

It presents a novel correlation inequality for Cauchy measures and introduces a new method involving spherical transport to analyze such inequalities.

Findings

Established a correlation inequality for Cauchy type measures.

Solved specific cases on the Riemannian sphere.

Proposed a new approach that can be extended to other problems.

Abstract

In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation problem. This method, as we shall explain, opens up a new class of interesting problems related to correlation type inequalities.