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On the Law of Addition of Random Matrices

✍ Scribed by L. Pastur; V. Vasilchuk

Publisher: Springer
Year: 2000
Tongue: English
Weight: 243 KB
Volume: 214
Category: Article
ISSN: 0010-3616
DOI: 10.1007/s002200000264

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Let M = m ij be a random n × n matrix over GF(2). Each matrix entry m ij is independently and identically distributed, with Pr m ij = 0 = 1 -p n and Pr m ij = 1 = p n . The probability that the matrix M is nonsingular tends to c 2 ≈ 0 28879 provided min p 1 -p ≥ log n + d n /n for any d n → ∞. Sharp