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Kesten-McKay law for the Markoff surface mod p

Courcy-Ireland, Matthew de; Magee, Michael

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Matthew de Courcy-Ireland


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.


Courcy-Ireland, M. D., & Magee, M. (2021). Kesten-McKay law for the Markoff surface mod p. Annales Henri Lebesgue, 4, 227-250.

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


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