Typical rank of coin-toss power-law random matrices over GF(2)
Disordered Systems and Neural Networks
2010-11-09 v1
Abstract
Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational optimization to complex networks. They are often approached using random matrices with Poisson-distributed or finite column/row-sums. This technical note considers the typical rank of random matrices belonging to a specific ensemble wich has genuinely power-law distributed column-sums. For this ensemble, we find a formula for calculating the typical rank in the limit of large matrices as a function of the power-law exponent and the shape of the matrix, and characterize its behavior through "phase diagrams" with varying model parameters.
Keywords
Cite
@article{arxiv.1011.1563,
title = {Typical rank of coin-toss power-law random matrices over GF(2)},
author = {Salvatore Mandrà and Marco Cosentino Lagomarsino and Bruno Bassetti},
journal= {arXiv preprint arXiv:1011.1563},
year = {2010}
}