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A theorem on the distribution of the rank of a sparse Boolean random matrix and some applications
Author(s):
V.
I.
Masol;
S.
V.
Popereshnyak
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 76
(2007).
Journal:
Theor. Probability and Math. Statist.
No. 76
(2008),
103-116.
MSC (2000):
Primary 68U20;
Secondary 60G10
Posted:
July 14, 2008
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Additional information
Abstract:
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.
References:
-
- 1.
- G. V. Balakin, The distribution of the rank of random matrices over a finite field, Teor. Verojatnost. i Primenen. XIII (1968), no. 4, 631-641; English transl. in Theor. Probab. Appl. 13 (1968), no. 4, 594-605. MR 0243571 (39:4892)
- 2.
- V. F. Kolchin, Random Graphs, Fizmatlit, Moscow, 2000, 256 pp. (Russian) MR 1812261 (2002e:60014)
- 3.
- V. I. Masol, Moments of the number of solutions of a system of random Boolean equations, Random Oper. Stochastic Equations 1 (1993), no. 2, 171-179. MR 1254185 (94h:60089)
- 4.
- V. I. Masol, Invariance theorems for systems of random Boolean equations, Sixth Intern. Vilnius Conf. of Probability Theory and Math. Statist., Abstracts of Communications, 1993, pp. 19-20.
- 5.
- B. A. Sevast'yanov, A Course in Probability Theory and Mathematical Statistics, ``Nauka'', Moscow, 1982. (Russian) MR 712294 (85a:60006)
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Additional Information:
V.
I.
Masol
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
vimasol@ukr.net
S.
V.
Popereshnyak
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
Popereshnyak_sv@mail.ru
DOI:
10.1090/S0094-9000-08-00735-7
PII:
S 0094-9000(08)00735-7
Keywords:
Boolean random matrix,
rank of a matrix,
the probability that a system is consistent,
the rate of convergence of distributions
Received by editor(s):
27/DEC/2005
Posted:
July 14, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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