Singularity Probabilities for Random Matrices over Finite Fields

Authors:
Jeff Kahn;János Komlós
Affiliations:
Department of Mathematics and RUTCOR, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: jkahn@math.rutgers.edu);Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: komlos@math.rutgers.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2001

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Abstract

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,****** Insert formula here ******