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oai:drops-oai.dagstuhl.de:18879 2024-03-06T11:02:49Z ddc:004 open_access

The Full Rank Condition for Sparse Random Matrices Coja-Oghlan, Amin Gao, Jane Hahn-Klimroth, Max Lee, Joon Müller, Noela Rolvien, Maurice random matrices rank finite fields rationals We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. Inspired by low-density parity check codes, the family of random matrices that we investigate is very general and encompasses both matrices over finite fields and {0,1}-matrices over the rationals. The proof combines statistical physics-inspired coupling techniques with local limit arguments. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Amin Coja-Oghlan and Jane Gao and Max Hahn-Klimroth and Joon Lee and Noela Müller and Maurice Rolvien 2023 Is Part Of LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2023.54 urn:nbn:de:0030-drops-188792 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.54 eng https://creativecommons.org/licenses/by/4.0/legalcode