Essentially Every Unimodular Matrix Defines and Expander

Authors:
Jin-yi Cai
Affiliations:
-
Venue:
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Year:
2000

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Abstract

We generalize the construction of Gabber and Galil to essentially every unimodular matrix in SL2(Z). It is shown that every parabolic or hyperbolic fractional linear transformation explicitly defines an expander of bounded degree and constant expansion. Thus all but a vanishingly small fraction of unimodular matrices define expanders.