A theorem on the distribution of the rank of a sparse Boolean random matrix and some applications. (Ukrainian, English) Zbl 1199.60028

Masol, V. I.; Popereshnyak, S. V.

Teor. Jmovirn. Mat. Stat. 76, 92-104 (2007); translation in Theory Probab. Math. Stat. 76, 103-116 (2008).

Summary: We consider some estimates of the rate of convergence of the distribution of a sparse Boolean random matrix to the Poisson distribution. The results obtained in the paper are applied to estimate the probability that a nonhomogeneous system of Boolean random linear equations is consistent.

MSC:

60C05	Combinatorial probability
15B52	Random matrices (algebraic aspects)
60F17	Functional limit theorems; invariance principles

Keywords:

sparse Boolean random matrix; Poisson distribution; rate of convergence

Citations:

Zbl 0184.41602; Zbl 0997.05001; Zbl 0842.60009