Topological characteristics of random triangulated surfaces

Authors:
Nicholas Pippenger;Kristin Schleich
Affiliations:
Department of Computer Science, Princeton University, Princeton, New Jersey 08544, USA;Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
Venue:
Random Structures & Algorithms
Year:
2006

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Abstract

We consider the topological characteristics of orientable surfaces generated by randomly gluing n triangles together. Our results are most conveniently expressed in terms of a parameter h = n / 2 + χ, where χ is the Euler characteristic of the surface. Simulations and results for similar models suggest that Ex [h] = log(3n) + γ + o(1) and Var [h] = log(3n) + γ - π2 / 6 + o(1). We prove that Ex [h] = log n + O(1) and Var [h] = O(log n). We also derive results concerning a number of other topological invariants and combinatorial characteristics of these random surfaces. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006