Outputs (4)

Random Unitary Representations of Surface Groups I: Asymptotic expansions (2021)
Journal Article
Magee, M. (2022). Random Unitary Representations of Surface Groups I: Asymptotic expansions. Communications in Mathematical Physics, 391(1), 119-171. https://doi.org/10.1007/s00220-021-04295-5

In this paper, we study random representations of fundamental groups of surfaces into special unitary groups. The random model we use is based on a symplectic form on moduli space due to Atiyah, Bott and Goldman. Let Σg denote a topological surface o... Read More about Random Unitary Representations of Surface Groups I: Asymptotic expansions.

Surface Words are Determined by Word Measures on Groups (2021)
Journal Article
Magee, M., & Puder, D. (2021). Surface Words are Determined by Word Measures on Groups. Israel Journal of Mathematics, 241, 749-774. https://doi.org/10.1007/s11856-021-2113-5

Every word w in a free group naturally induces a probability measure on every compact group G. For example, if w = [x, y] is the commutator word, a random element sampled by the w-measure is given by the commutator [g, h] of two independent, Haar-ran... Read More about Surface Words are Determined by Word Measures on Groups.

Random Unitary Representations of Surface Groups II: The large n limit [preprint] (2021)
Preprint / Working Paper
Magee, M. Random Unitary Representations of Surface Groups II: The large n limit [preprint]

Kesten-McKay law for the Markoff surface mod p (2021)
Journal Article
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

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 pro... Read More about Kesten-McKay law for the Markoff surface mod p.