2022/10/24 by Marcos Mariño, Ricardo Schiappa, Marino, Marcos +3 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2210.13479
openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The complete, nonperturbative content of random matrix models is described by resurgent-transseries -- general solutions to their corresponding string-equations. These transseries include exponentially-suppressed multi-instanton amplitudes obtained by eigenvalue tunneling, but they also contain exponentially-enhanced and mixed instanton-like sectors with no known matrix model interpretation. This work shows how these sectors can be also described by eigenvalue tunneling in matrix models -- but on the non-physical sheet of the spectral curve describing their large-N limit. This picture further explains the full resurgence of random matrices via analysis of all possible eigenvalue integration-contours. How to calculate these "anti" eigenvalue-tunneling amplitudes is explained in detail and in various examples, such as the cubic and quartic matrix models, and their double-scaling limit to Painleve I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques.