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math.DG2005★ 1 cited
The length of closed geodesics on random Riemann Surfaces
Eran Makover, Jeffrey McGowan
Short geodesics are important in the study of the geometry and the spectra of Riemann surfaces. Bers' theorem gives a global bound on the length of the first geodesics. We u…
math.DG2001
Random Construction of Riemann Surfaces
Robert Brooks, Eran Makover
In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? We do so by constructing compact Riemann surfa…
math.DG2001
On the Genus of a Random Riemann Surface
Alexander Gamburd, Eran Makover
Brooks and Makover introduced an approach to random Riemann surfaces based on associating a dense set of them - Belyi surfaces - with random cubic graphs. In this paper, using Boll…