Three-point correlations for quantum star graphs

TL;DR

This paper calculates the three-point eigenvalue correlation function for quantum star graphs with many edges, extending previous work on two-point correlations and revealing non-Poisson, non-random matrix statistics.

Contribution

It introduces a method to compute three-point correlations on quantum star graphs, expanding the understanding of their spectral statistics beyond two-point functions.

Findings

Three-point correlation function computed for quantum star graphs.

Eigenvalue statistics deviate from Poisson and random matrix models.

Method uses trace formula and combinatorial analysis.

Abstract

We compute the three point correlation function for the eigenvalues of the Laplacian on quantum star graphs in the limit where the number of edges tends to infinity. This extends a work by Berkolaiko and Keating, where they get the 2-point correlation function and show that it follows neither Poisson, nor random matrix statistics. It makes use of the trace formula and combinatorial analysis.