SciPost Physics· 2026Q1
New instantons for matrix models
- 12citations
- Q1SCImago
- 2026year
Short summary
This paper reveals that exponentially-enhanced and mixed instanton-like sectors in random matrix models, previously lacking interpretation, can be described by eigenvalue tunneling on the non-physical sheet of the spectral curve.
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Key points
- Exponentially-enhanced and mixed instanton-like sectors in random matrix models are now interpretable.
- These sectors are described by eigenvalue tunneling on the non-physical sheet of the spectral curve.
- This finding explains the full resurgence of random matrices via analysis of all eigenvalue integration contours.
- Methods for calculating these "anti" tunneling amplitudes are provided with examples (cubic, quartic models, Painlevé I).
AI-generated from the title and abstract; the full text is not read.
Abstract
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 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 Painlevé I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques.
The authors' abstract, as published at the source. SciPost Physics, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics