Determinantal identity for multilevel systems and finite determinantal processes

TL;DR

This paper presents a straightforward algebraic derivation of a determinantal identity applicable to multilevel systems like random matrix chains and finite determinantal point processes, aiding in calculating various statistical properties.

Contribution

It introduces a simple algebraic proof of a determinantal identity that facilitates analysis of multilevel systems and finite determinantal processes.

Findings

Derivation of a useful determinantal identity for multilevel systems

Application to calculation of point correlators, gap probabilities, and Janossy densities

Simplifies analysis of random matrix chains and determinantal point processes

Abstract

We give a simple algebraic derivation of a useful determinantal identity for multilevel systems such as random matrix chains and finite determinantal point processes, with applications to the calculation of point correlators, gap probabililties and Janossy densities.