On the genus of a random Riemann surface

Alexander Gamburd, Eran Makover

Type: Other

Publication Date: 2002-01-01

Citations: 13

DOI: https://doi.org/10.1090/conm/311/05451

Abstract

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.

Locations

Contemporary mathematics - American Mathematical Society - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	On the Genus of a Random Riemann Surface	2001	Alexander Gamburd Eran Makover
+ PDF Chat	Random Construction of Riemann Surfaces	2004	Robert Brooks Eran Makover
+ PDF Chat	Poisson–Dirichlet distribution for random Belyi surfaces	2006	Alex Gamburd
+	Random Construction of Riemann Surfaces	2001	Robert Brooks Eran Makover
+	On the Genus of Random Regular Graphs	2022	Lucas Blakeslee
+	The Cheeger constants of random Belyi surfaces	2022	Yang Shen Yunhui Wu
+	Discrete Random Surfaces in High Genus	2023	Nicolas Curien
+ PDF Chat	The Cheeger Constants of Random Belyi Surfaces	2022	Yang Shen Yunhui Wu
+	Random graphs on surfaces	2008	Colin McDiarmid
+ PDF Chat	Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves	2022	Vincent Delecroix Élise Goujard Peter Zograf Anton Zorich
+	On the entropy of random surfaces with arbitrary genus	1987	Ivan Kostov A. Krzywicki
+ PDF Chat	Finite length spectra of random surfaces and their dependence on genus	2016	Bram Petri
+	Finite length spectra of random surfaces and their dependence on genus	2014	Bram Petri
+	Finite length spectra of random surfaces and their dependence on genus	2014	Bram Petri
+	Constructing Random Klein Surfaces Without Boundary	2018	Antonio F. Costa Eran Makover
+	On the Euler characteristics of random surfaces	1985	Robert Schrader
+	Large deviations and moments for the Euler characteristic of a random surface	2010	Kevin Fleming Nicholas Pippenger
+	Universality for random surfaces in unconstrained genus	2019	Thomas Budzinski Nicolas Curien Bram Petri
+	Universality for random surfaces in unconstrained genus	2019	Thomas Budzinski Nicolas Curien Bram Petri
+	The evolution of random graphs on surfaces	2017	Chris Dowden Mihyun Kang Philipp Sprüssel

Works That Cite This (12)

Action	Title	Year	Authors
+ PDF Chat	Random regular graphs and the systole of a random surface	2017	Bram Petri
+ PDF Chat	The topology and geometry of random square-tiled surfaces	2022	Sunrose T. Shrestha
+	Constructing Random Klein Surfaces Without Boundary	2018	Antonio F. Costa Eran Makover
+ PDF Chat	Géométrie et topologie des variétés hyperboliques de grand volume	2014	Jean Raimbault
+ PDF Chat	Pants Decompositions of Random Surfaces	2011	Larry Guth Hugo Parlier Robert M. Young
+ PDF Chat	Poisson–Dirichlet distribution for random Belyi surfaces	2006	Alex Gamburd
+ PDF Chat	Finite length spectra of random surfaces and their dependence on genus	2016	Bram Petri
+ PDF Chat	A Uniform Sampling Procedure for Abstract Triangulations of Surfaces	2023	Rajan Shankar Jonathan Spreer
+	Random Planar Geometry	2013	Itaı Benjamini
+ PDF Chat	The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations	2004	Persi Diaconis Eddy Mayer-Wolf Ofer Zeitouni Martin Zerner

Works Cited by This (3)

Action	Title	Year	Authors
+	The Isoperimetric Number of Random Regular Graphs	1988	Béla Bollobás
+	On the average genus of the random graph	1995	Saul Stahl
+	ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD	1980	G. V. Belyi