The rank of sparse random matrices

Alperen A. Ergür
Alperen A. Ergür
Samuel Hetterich
Samuel Hetterich
Maurice Rolvien
Maurice Rolvien
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Abstract:

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 entri...More

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