On the Genus of a Random Riemann Surface

Details On the Genus of a Random Riemann Surface On the Genus of a Random Riemann Surface

2001-04-03

arxiv.org/abs/math/0104038v1

Mathematics

Differential Geometry

Scientific paper

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.

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