On the Rank of Random Sparse Matrices

DOI10.1017/S0963548309990447zbMath1204.15042arXiv0711.2696OpenAlexW2117991835MaRDI QIDQ3058294

Van H. Vu, Kevin P. Costello

Publication date: 19 November 2010

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2696

zbMATH Keywords

rankBernoulli random variablescomplex symmetric matrixrandom sparse matricesmatrix co-rank

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (9)

Singularity of sparse random matrices: simple proofs ⋮ Hitting Time Theorems for Random Matrices ⋮ Singularity of the \(k\)-core of a random graph ⋮ Combinatorics. Abstracts from the workshop held January 1--7, 2023 ⋮ The rank of random graphs ⋮ Sharp transition of the invertibility of the adjacency matrices of sparse random graphs ⋮ On the universality of the non-singularity of general Ginibre and Wigner random matrices ⋮ Recent progress in combinatorial random matrix theory ⋮ The rank of sparse random matrices

Cites Work

• Random symmetric matrices are almost surely nonsingular.
• The rank of random graphs
• Estimates for the concentration function of combinatorial number theory and probability
• On a lemma of Littlewood and Offord

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