Positroids have the Rayleigh property

TL;DR

This paper proves that positroids, a special class of matroids with recent mathematical and physical applications, possess the Rayleigh property, a negative correlation property originally from electrical network theory.

Contribution

It establishes that positroids have the Rayleigh property, extending the class of matroids known to exhibit this negative correlation characteristic.

Findings

Positroids have the Rayleigh property.

This extends the understanding of negative correlation in matroids.

Supports applications of positroids in math and physics.

Abstract

The Rayleigh property is a negative correlation property of electrical networks, which was generalized to matroids by Choe and Wagner. We prove that positroids, a class of matroid introduced by Postnikov which have seen many recent applications in both math and physics, have the Rayleigh property.