Singularity of random symmetric matrices revisited

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Colleges, School and Institutes


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(nlogn)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.

Bibliographic note

Not yet published as of 26/08/2021.


Original languageEnglish
JournalProceedings of the American Mathematical Society
Publication statusAccepted/In press - 3 Aug 2021


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