Random Antagonistic Matrices

TL;DR

This paper introduces and studies antagonistic matrices, a generalization of antisymmetric matrices with applications in modeling competitive species dynamics in ecology.

Contribution

The paper defines antagonistic matrices, explores their properties, and connects them to ecological models, extending the class of matrices used in such analyses.

Findings

Antagonistic matrices generalize antisymmetric matrices.

They model competitive interactions with opposite signs.

Applications to ecological dynamics are demonstrated.

Abstract

The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries $\mathcal A_{i,j}$ and $\mathcal A_{j,i}$ are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology.