Stein’s method and the rank distribution of random matrices over finite fields

• Fulman, Jason ^[1] ; Goldstein, Larry ^[1]
  1. [1] University of Southern California

     University of Southern California

     Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 3, 2015, págs. 1274-1314
• Idioma: inglés
• DOI: 10.1214/13-AOP889
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• Resumen

  • With Qq,n the distribution of n minus the rank of a matrix chosen uniformly from the collection of all n×(n+m) matrices over the finite field Fq of size q≥2, and Qq the distributional limit of Qq,n as n→∞ , we apply Stein’s method to prove the total variation bound 18qn+m+1≤∥Qq,n−Qq∥TV≤3qn+m+1.

    In addition, we obtain similar sharp results for the rank distributions of symmetric, symmetric with zero diagonal, skew symmetric, skew centrosymmetric and Hermitian matrices.