Paper Info
Title
On the distribution of rank of a random matrix over a finite field
Abstract
Let M = (m(ij)) be a random n x n matrix over GF(t) in which each matrix entry m(ij) is independently and identically distributed, with Pr(m(ij) = 0) = 1 - p(n) and Pr(m(ij) = r) = p(n)/(t - 1), r not equal 0. If we choose t greater than or equal to 3, and condition on M having no zero rows or columns, then the probability that M is nonsingular tends to c(t) similar to Pi (infinity)(j=1)(1 - t(-j)) provided p greater than or equal to (log n + d)/n, where d --> -infinity slowly. (C) 2000 John Wiley & Sons, Inc.
Year
DOI
Venue
2000
10.1002/1098-2418(200010/12)17:3/4<197::AID-RSA2>3.0.CO;2-K
Random Struct. Algorithms
Keywords
Field
DocType
random matrix,finite field,independent and identically distributed
Discrete mathematics,Binary logarithm,Combinatorics,Finite field,Matrix (mathematics),Independent and identically distributed random variables,Mathematics,Random matrix
Journal
Volume
Issue
ISSN
17
3-4
1042-9832
Citations 
PageRank 
References 
32
1.73
2
Authors
1
Name
Order
Citations
PageRank
Colin Cooper128730.73