# Identifiability of parametric random matrix models

## TL;DR

This paper studies whether the parameters of certain random matrix models can be uniquely determined from their spectral distributions, using free probability theory to establish conditions for identifiability.

## Contribution

It demonstrates that compound Wishart and signal-plus-noise models are identifiable up to rotation, advancing understanding of parameter recovery in spectral analysis.

## Key findings

- Models are identifiable up to rotation.
- Free probability theory is effective for analyzing identifiability.
- Provides theoretical conditions for parameter uniqueness.

## Abstract

We investigate parameter identifiability of spectral distributions of random matrices. In particular, we treat compound Wishart type and signal-plus-noise type. We show that each model is identifiable up to some kind of rotation of parameter space. Our method is based on free probability theory.