Random discrete groups in the space of Möbius transformations : a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealand

Abstract

Discrete subgroups of random Möbius transformations are investigated using computational methods together with collateral mathematical analysis. The main results include quantification of the likelihood of occurrence of two generator discrete groups and studies of the sharpness of the Hadamard inequality for random matrices and of the scale invariance for the domain of definition for matrix entry distributions derived by normalisation of matrices in GL(2,C) to SL(2,C).