The rank of sparse random matrices

06/13/2019

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by   Amin Coja-Oghlan, et al.

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Generalising prior work on the rank of random matrices over finite fields [Coja-Oghlan and Gao 2018], we determine the rank of a random matrix with prescribed numbers of non-zero entries in each row and column over any field. The rank formula turns out to be independent of both the field and the distribution of the non-zero matrix entries. The proofs are based on a blend of algebraic and probabilistic methods inspired by ideas from mathematical physics.