Singularity of random symmetric matrices revisited

Marcelo Campos, Matthew Jenssen, Marcus Michelen, Julian Sahasrabudhe

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Let Mn be drawn uniformly from all ±1 symmetric n×n matrices. We show that the probability that Mn is singular is at most exp(−c(n log n)1/2), which represents a natural barrier in recent approaches to this problem. In addition to improving on the best-known previous bound of Campos, Mattos, Morris and Morrison of exp(−cn1/2) on the singularity probability, our method is different and considerably simpler: we prove a “rough” inverse Littlewood-Offord theorem by a simple combinatorial iteration.
Original languageEnglish
JournalProceedings of the American Mathematical Society
Early online date24 Mar 2022
Publication statusE-pub ahead of print - 24 Mar 2022


  • math.PR
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