Year: 2025
Type: article
Abstract: We analyze the asymptotic properties a special solution of the (3, 4) string equation, which appears in the study of the multicritical quartic 2-matrix model. In particular, we show that in a certain parameter regime, the corresponding τ -function has an asymptotic expansion which is ‘topological’ in nature. Consequently, we show that this solution to the string equation with a specific set of Stokes data exists, at least asymptotically. We also demonstrate that, along specific curves in the parameter space, this τ -function degenerates to the τ -function for a tritronquée solution of Painlevé I (which appears in the critical quartic 1-matrix model), indicating that there is a ‘renormalization group flow’ between these critical points. This confirms a conjecture from Crnković et al (1990 Phys. Lett. B 237 196–201).
Author: Nathan Hayford
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Award: Patterns in Random Tilings
OpenAlex ID: W4415004810