Abstract
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 language | English |
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Journal | Proceedings of the American Mathematical Society |
Early online date | 24 Mar 2022 |
DOIs | |
Publication status | E-pub ahead of print - 24 Mar 2022 |
Keywords
- math.PR
- math.CO