### Abstract

Original language | English |
---|---|

Article number | P04017 |

Pages (from-to) | P04017 |

Journal | Journal of Statistical Mechanics |

Volume | 2009 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2009 |

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### Bibliographical note

Copyright of the Institute of Physics### Keywords

- random graphs
- networks
- new applications of statistical mechanics
- random matrix theory and extensions

### Cite this

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*Journal of Statistical Mechanics*, vol. 2009, no. 4, P04017, pp. P04017. https://doi.org/10.1088/1742-5468/2009/04/P04017

**Properties of sparse random matrices over finite fields.** / Alamino, Roberto C.; Saad, David.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Properties of sparse random matrices over finite fields

AU - Alamino, Roberto C.

AU - Saad, David

N1 - Copyright of the Institute of Physics

PY - 2009/4

Y1 - 2009/4

N2 - 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.

AB - 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.

KW - random graphs

KW - networks

KW - new applications of statistical mechanics

KW - random matrix theory and extensions

UR - http://www.scopus.com/inward/record.url?scp=70449416162&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2009/04/P04017

DO - 10.1088/1742-5468/2009/04/P04017

M3 - Article

VL - 2009

SP - P04017

JO - Journal of Statistical Mechanics

JF - Journal of Statistical Mechanics

SN - 1742-5468

IS - 4

M1 - P04017

ER -