Typical rank of coin-toss power-law random matrices over GF(2)

Details Typical rank of coin-toss power-law random matrices over GF(2) Typical rank of coin-toss power-law random matrices over GF(2)

2010-11-06

arxiv.org/abs/1011.1563v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

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.

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