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Mathematics of Computation

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How to pick a random integer matrix? (and other questions)

Author: Igor Rivin
Journal: Math. Comp. 85 (2016), 783-797
MSC (2010): Primary 20H05, 20P05, 20G99
Published electronically: June 17, 2015
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Abstract: We discuss the question of how to pick a matrix uniformly (in an appropriate sense) at random from groups big and small. We give algorithms in some cases, and indicate interesting problems in others.

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Additional Information

Igor Rivin
Affiliation: School of Mathematics, University of St Andrews, St Andrews, UK
Address at time of publication: Department of Mathematics, Temple University, Philadelphia, Pennsylvania

Keywords: Groups, lattices, matrices, randomness, probability
Received by editor(s): February 15, 2014
Received by editor(s) in revised form: July 6, 2014, and August 19, 2014
Published electronically: June 17, 2015
Additional Notes: The author would like to thank Nick Katz , Chris Hall, Peter Sarnak, and Hee Oh for helpful conversations. He would also like to thank ICERM and Brown University for their hospitality and generous support. The author would like to thank the anonymous referees for their patience and helpful suggestions.
Article copyright: © Copyright 2015 American Mathematical Society