# Random matrices and the New York City subway system

## TL;DR

This paper investigates the statistical properties of subway train arrival times in NYC, revealing regimes where the gaps follow random matrix or Poisson statistics, influenced by Coulomb potential and number of stops.

## Contribution

It introduces a novel analysis linking train arrival statistics to random matrix theory and Coulomb potential, highlighting how operational factors affect these regimes.

## Key findings

- Gaps between trains follow random matrix and Poisson statistics.
- Departure from random matrix behavior correlates with Coulomb potential.
- More stops increase deviation from random matrix statistics.

## Abstract

We analyze subway arrival times in the New York City subway system. We find regimes where the gaps between trains exhibit both (unitarily invariant) random matrix statistics and Poisson statistics. The departure from random matrix statistics is captured by the value of the Coulomb potential along the subway route. This departure becomes more pronounced as trains make more stops.