SINGULARITY OF RANDOM SYMMETRIC MATRICES—A COMBINATORIAL APPROACH TO IMPROVED BOUNDS

DOI10.1017/fms.2019.21zbMath1423.60016arXiv1809.04718OpenAlexW2890959015MaRDI QIDQ5197490

Asaf Ferber, Vishesh Jain

Publication date: 24 September 2019

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.04718

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Inverse Littlewood-Offord problems and the singularity of random symmetric matrices
• Optimal inverse Littlewood-Offord theorems
• Random symmetric matrices are almost surely nonsingular.
• John-type theorems for generalized arithmetic progressions and iterated sumsets
• On the singularity probability of discrete random matrices
• On subspaces spanned by random selections of \(\pm 1\) vectors
• Approximate Spielman-Teng theorems for the least singular value of random combinatorial matrices
• Singularity of random Bernoulli matrices
• The Littlewood-Offord problem and invertibility of random matrices
• Non-asymptotic theory of random matrices: extreme singular values
• On the singularity probability of random Bernoulli matrices
• Estimates for the concentration function of combinatorial number theory and probability
• On the Probability That a Random ± 1-Matrix Is Singular
• On the counting problem in inverse Littlewood–Offord theory
• Invertibility of symmetric random matrices
• Small Ball Probability, Inverse Theorems, and Applications