On the rank of random matrices
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Let M = mij be a random n × n matrix over GF(2). Each matrix entry mij is independently and identically distributed, with Prmij = 0 = 1 − pn and Prmij = 1 = pn. The probability that the matrix M is nonsingular tends to c2 ≈ 0:28879 provided minp; 1− p ≥ log n+ dn/n for any dn → ∞. Sharp thresholds are also obtained for constant dn. This answers a question posed in a paper by J. Blömer, R. Karp, and E. Welzl (Random Struct Alg, 10(4) (1997)). © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 209–232, 2000
[1] Richard M. Karp,et al. The rank of sparse random matrices over finite fields , 1997 .
[2] V. F. Kolchin,et al. Random Graphs and Systems of Linear Equations in Finite Fields , 1994, Random Struct. Algorithms.
[3] Richard M. Wilson,et al. A course in combinatorics , 1992 .
[4] R. Durrett. Probability: Theory and Examples , 1993 .