Properties of sparse random matrices over finite fields

Alamino, Roberto C. and Saad, David (2009). Properties of sparse random matrices over finite fields. Journal of Statistical Mechanics, 2009 (4), P04017.


Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Divisions: ASTON EPrints organisational structure > Schools_of_Study > Engineering & Applied Science > Mathematics (EAS)
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Additional Information: Copyright of the Institute of Physics
Uncontrolled Keywords: random graphs,networks,new applications of statistical mechanics,random matrix theory and extensions,Statistics and Probability,Statistical and Nonlinear Physics,Statistics, Probability and Uncertainty
Published Date: 2009-04



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