# Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrum

## TL;DR

This paper generalizes formulas for the spectrum of polynomials in cyclic monotone elements and applies these results to analyze random matrices with discrete spectra.

## Contribution

It offers new proofs and a broader generalization of existing spectral formulas for cyclic monotone elements, with applications to random matrix theory.

## Key findings

- Extended spectral formulas for cyclic monotone elements.
- New proofs simplifying previous results.
- Application to random matrices with discrete spectrum.

## Abstract

We provide a generalization and new proofs of the formulas of Collins, Hasebe and Sakuma for the spectrum of polynomials in cyclic monotone elements. This is applied to random matrices with discrete spectrum.