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On the Rank of Random Sparse Matrices

Published online by Cambridge University Press:  12 October 2009

KEVIN P. COSTELLO  and
VAN VU
KEVIN P. COSTELLO
Affiliation:
Department of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA (e-mail kcostell@math.gatech.edu)
VAN VU
Affiliation:
Department of Mathematics, Rutgers, Piscataway, NJ 08854, USA (e-mail vanvu@math.rutgers.edu)
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Abstract

We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This allows us to obtain an exact estimate for the co-rank.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 19 , Issue 3 , May 2010 , pp. 321 - 342
Copyright
Copyright © Cambridge University Press 2009

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References

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