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Singularity Probabilities for Random Matrices over Finite Fields

Published online by Cambridge University Press:  24 May 2001

JEFF KAHN  and
JÁNOS KOMLÓS
JEFF KAHN
Affiliation:
Department of Mathematics and RUTCOR, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: jkahn@math.rutgers.edu)
JÁNOS KOMLÓS
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: komlos@math.rutgers.edu)
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Abstract

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Fix q and let Mn be an n × n matrix with entries drawn independently from the finite field Fq according to some distribution μn. It is shown that, except in certain pathological cases, the probability that Mn is nonsingular is asymptotically the same as for uniform entries; that is,

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Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 2 , March 2001 , pp. 137 - 157
Copyright
2001 Cambridge University Press