2001/04/03 by Alexander Gamburd, Gamburd, Alexander, Eran Makover +1
Mathematics · #05C10 #05C80 #30F99 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Spectral Theory (math.SP) #math.DG #math.SP #msc:05C10 #msc:05C80 #msc:30F99 #msc:58J50
paper · pdf · doi:10.48550/arxiv.math/0104038
arxiv created 2001/04/03 · openalex publication_date 2001/04/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Bollobas model for random regular graphs, we examine the topological structure of these surfaces, obtaining in particular an estimate for the expected value of their genus.