# Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory

## TL;DR

This paper reveals a new universality in large chaotic systems where the Lyapunov spectrum's statistical properties align with Random Matrix Theory, demonstrated through models related to black holes and matrix products.

## Contribution

It introduces the concept of universality in Lyapunov spectra for large chaotic systems and connects it to Random Matrix Theory, with evidence from stringy black hole models and random matrix products.

## Key findings

- Lyapunov spectra follow RMT statistics in large chaotic systems.
- Universal behavior appears immediately in the massless limit.
- Universal patterns emerge at late times in other models.

## Abstract

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.