Algorithms and Computation

Volume 1969 of the series Lecture Notes in Computer Science pp 2-22


Essentially Every Unimodular Matrix Defines an Expander

  • Jin-Yi CaiAffiliated withDepartment of Computer Science and Engineering, State University of New York at BuffaloComputer Sciences Department, University of Wisconsin

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We generalize the construction of Gabber and Galil to essentially every unimodular matrix in SL 2(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.