# Probing Black Hole Microstate Evolution with Networks and Random Walks

## TL;DR

This paper models black hole microstates using network theory and identifies three distinct late-time behavioral phases, revealing complex emergent properties beyond simple entropic predictions.

## Contribution

It introduces a novel network-based approach to analyze black hole microstate evolution and identifies phases of late-time behavior linked to microstate connectivity.

## Key findings

- Identifies three phases: ergodic, trapped, amplified.
- Shows late-time properties depend on microstate connectivity.
- Highlights non-trivial emergent properties of microstates.

## Abstract

We model black hole microstates and quantum tunneling transitions between them with networks and simulate their time evolution using well-established tools in network theory. In particular, we consider two models based on Bena-Warner three-charge multi-centered microstates and one model based on the D1-D5 system; we use network theory methods to determine how many centers (or D1-D5 string strands) we expect to see in a typical late-time state. We find three distinct possible phases in parameter space for the late-time behaviour of these networks, which we call ergodic, trapped, and amplified, depending on the relative importance and connectedness of microstates. We analyze in detail how these different phases of late-time behavior are related to the underlying physics of the black hole microstates. Our results indicate that the expected properties of microstates at late times cannot always be determined simply by entropic arguments; typicality is instead a highly non-trivial, emergent property of the full Hilbert space of microstates.