Stein’s method and the rank distribution of random matrices over finite fields
نویسندگان
چکیده
With Qq,n the distribution of n minus the rank of a matrix Mn chosen uniformly from Mat(n, q), the collection of all n × n 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 1 8qn+1 ≤ ||Qq,n −Qq||TV ≤ 3 qn+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.
منابع مشابه
STEIN’S METHOD AND THE RANK DISTRIBUTION OF RANDOM MATRICES OVER FINITE FIELDS BY JASON FULMAN1 AND LARRY GOLDSTEIN2 University of Southern California
With Q q,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 F q of size q ≥ 2, and Q q the distributional limit of Q q,n as n → ∞, we apply Stein's method to prove the total variation bound 1 8q n+m+1 ≤ ≤Q q,n − Q q TV ≤ 3 q n+m+1. In addition, we obtain similar sharp results for the rank distributions of sym...
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