Singularity Probabilities for Random Matrices over Finite Fields

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Abstract

Fix q and let Mn be an n x n matrix with entries drawn independently from the finite field Fq according to some distribution μn. It is shown that, except in certain pathological cases, the probability that Mn is nonsingular is asymptotically the same as for uniform entries; that is, Pr(Mn is nonsingular) Πi≥1 (1 - q-i) as n → ∞.

Original languageEnglish (US)
Pages (from-to)137-157
Number of pages21
JournalCombinatorics Probability and Computing
Volume10
Issue number2
DOIs
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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