Random matrix statistics and safety rest areas on interstates in the United States

TL;DR

This study applies random matrix theory to analyze the spacing of safety rest areas on US interstates, revealing universal statistical patterns and regional differences influenced by geography and economics.

Contribution

It demonstrates that safety rest area spacings follow Wigner surmise statistics, linking physical spacing patterns to random matrix theory and regional traits.

Findings

Rest area spacings follow Wigner surmise statistics.

Regional traits influence spacing distributions, with Poissonian patterns emerging in certain areas.

Geographical obstacles correlate with more Poissonian spacing patterns.

Abstract

We analyze physical spacings between locations of safety rest areas on interstates in the United States. We show normalized safety rest area spacings on major interstates exhibit Wigner surmise statistics, which align with the eigenvalue spacings for the Gaussian Unitary Ensemble from random matrix theory as well as the one-dimensional gas interactions via the Coulomb potential. We identify economic and geographic regional traits at the state level that exhibit Poissonian statistics, which become more pronounced with increased geographical obstacles in interstate travel. Other regional filters (e.g., historical or political) produced results that did not diverge substantially from the overall Wigner surmise model.