Graduation Year
2008
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Nicholas Pippenger
Reader 2
Francis Edward Su
Abstract
Random triangulated surfaces are created by taking an even number, n, of triangles and arbitrarily ”gluing” together pairs of edges until every edge has been paired. The resulting surface can be described in terms of its number of boundary cycles, a random variable denoted by h. Building upon the work of Nicholas Pippenger and Kristin Schleich, and using a recent result from Alex Gamburd, we establish an improved approximation for the expectation of h for certain values of n. We use a computer simulation to exactly determine the distribution of h for small values of n, and present a method for calculating these probabilities. We also conduct an investigation into the related problem of creating one connected component out of n triangles.
Recommended Citation
Fleming, Kevin, "Boundary Cycles in Random Triangulated Surfaces" (2008). HMC Senior Theses. 205.
https://scholarship.claremont.edu/hmc_theses/205
