Kesten-McKay law for the Markoff surface mod p

Courcy-Ireland, Matthew de; Magee, Michael

doi:10.5802/ahl.71

Kesten-McKay law for the Markoff surface mod p

Courcy-Ireland, Matthew de; Magee, Michael

Authors

Matthew de Courcy-Ireland

Professor Michael Magee michael.r.magee@durham.ac.uk
Professor

Abstract

For each prime p, we study the eigenvalues of a 3-regular graph on roughly vertices constructed from the Markoff surface. We show they asymptotically follow the Kesten–McKay law, which also describes the eigenvalues of a random regular graph. The proof is based on the method of moments and takes advantage of a natural group action on the Markoff surface.

Citation

Courcy-Ireland, M. D., & Magee, M. (2021). Kesten-McKay law for the Markoff surface mod p. Annales Henri Lebesgue, 4, 227-250. https://doi.org/10.5802/ahl.71

Journal Article Type	Article
Acceptance Date	May 1, 2020
Publication Date	Jan 1, 2021
Deposit Date	May 12, 2020
Publicly Available Date	Nov 7, 2022
Journal	Annales Henri Lebesgue
Publisher	École Normale Supérieure de Rennes
Peer Reviewed	Peer Reviewed
Volume	4
Pages	227-250
DOI	https://doi.org/10.5802/ahl.71