The singularity probability of a random symmetric matrix is exponentially small

Marcelo Campos, Matthew Jenssen, Marcus Michelen, Julian Sahasrabudhe

Research output: Working paper/PreprintPreprint

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Abstract

Let A be drawn uniformly at random from the set of all n × n symmetric matrices with entries in {−1, 1}. We show that P(det(A) = 0) 6 e −cn , where c > 0 is an absolute constant, thereby resolving a well-known conjecture.
Original languageEnglish
Publication statusPublished - 24 May 2021

Bibliographical note

51 pages. Sections 3+4 split up and reorganized and proof sketch expanded

Keywords

  • math.PR
  • math.CO

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