Publication Date

Spring 2026

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Physics and Astronomy

Advisor

Curtis Asplund; Hilary Hurst; Kassahun Betre

Abstract

This thesis investigates connections between random matrix theory and low-dimensional quantum gravity through the spectral form factor (SFF), a well-studied function that characterizes correlations in the eigenvalue spectrum of an operator. In random matrix ensembles, a feature of the SFF known as the “ramp” is governed by universal spectral correlations, and in Jackiw–Teitelboim (JT) gravity this regime is due to the double-trumpet wormhole geometry. We study the connected correlation functions underlying the SFF using combinatorial, diagrammatic methods from a mathematical formalism known as second-order free probability theory, where they are expressed in terms of annular noncrossing permutations. To access a continuum description, we introduce a double-scaling limit in which both matrix size and moment order grow. This limit probes universal edge fluctuations of the spectrum. In this scaling regime, the discrete combinatorial sums admit a continuum limit whose structure matches that of the double-trumpet amplitude in JT gravity, expressed as an integral over geodesic lengths, up to normalization and scaling conventions. This provides a bridge between discrete combinatorial diagrams governing spectral correlations and geometric contributions to the gravitational path integral. Specifically, in this limit, there is a clear mapping between the boundary lengths and minimum geodesic length of the double-trumpet wormhole and the combinatorial parameters of annular non-crossing permutations. We extend this framework to time-reversal invariant ensembles, where additional diagrams contribute to the correlation functions, matching the behavior of an extension of JT gravity that includes integrating over nonorientable geometries. We discuss how this connection reframes puzzles in low-dimensional holography including ensemble averaging, factorization, and the nature of closed universe Hilbert spaces.

Download

Included in

Physics Commons

Share

COinS