Kesten-McKay law for the Markoff surface mod p

Courcy-Ireland, Matthew de; Magee, Michael

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