Hostname: page-component-cc8bf7c57-xrnlw Total loading time: 0 Render date: 2024-12-11T17:54:03.313Z Has data issue: false hasContentIssue false
  • English
  • Français

Singularity Probabilities for Random Matrices over Finite Fields

Published online by Cambridge University Press:  24 May 2001

JEFF KAHN  and
JÁNOS KOMLÓS
JEFF KAHN
Affiliation:
Department of Mathematics and RUTCOR, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: jkahn@math.rutgers.edu)
JÁNOS KOMLÓS
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: komlos@math.rutgers.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Fix q and let Mn be an n × 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,

[Formula here]

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 2 , March 2001 , pp. 137 - 157
Copyright
2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)