# The Kontsevich Matrix Integral: Convergence to the Painlevé Hierarchy and Stokes’ Phenomenon

@article{Bertola2017TheKM,
title={The Kontsevich Matrix Integral: Convergence to the Painlev{\'e} Hierarchy and Stokes’ Phenomenon},
author={Marco Bertola and Mattia Cafasso},
journal={Communications in Mathematical Physics},
year={2017},
volume={352},
pages={585-619}
}
• Published 2017
• Physics, Mathematics
• Communications in Mathematical Physics
• We show that the Kontsevich integral on $${n\times n}$$n×n matrices ($${n < \infty}$$n<∞) is the isomonodromic tau function associated to a $${2\times 2}$$2×2 Riemann–Hilbert Problem. The approach allows us to gain control of the analysis of the convergence as $${n\to\infty}$$n→∞. By an appropriate choice of the external source matrix in Kontsevich’s integral, we show that the limit produces the isomonodromic tau function of a special tronquée solution of the first Painlevé hierarchy, and we… CONTINUE READING