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Creators/Authors contains: "Campos, Marcelo"

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  1. ; ; ; (, Journal of the American Mathematical Society)
    Free, publicly-accessible full text available January 1, 2026
  2. ; ; ; (, Forum of Mathematics, Pi)
    Full Text Available 
  3. ; ; ; (, Proceedings of the American Mathematical Society)
    Let M n M_n be drawn uniformly from all ± 1 \pm 1 symmetric n × n n \times n matrices. We show that the probability that M n M_n is singular is at most exp ⁡ ( − c ( n log ⁡ n ) 1 / 2 ) \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 ⁡ ( − c n 1 / 2 ) \exp (-c n^{1/2}) on the singularity probability, our method is different and considerably simpler: we prove a “rough” inverse Littlewood-Offord theorem by a simple combinatorial iteration. 
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