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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

A theorem on the distribution of the rank of a sparse Boolean random matrix and some applications


Authors: V. I. Masol and S. V. Popereshnyak
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 76 (2007).
Journal: Theor. Probability and Math. Statist. 76 (2008), 103-116
MSC (2000): Primary 68U20; Secondary 60G10
Published electronically: July 14, 2008
MathSciNet review: 2368743
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Abstract | References | Similar Articles | 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 [Enhancements On Off] (What's this?)

  • 1. G. V. Balakin, The distribution of the rank of random matrices over a finite field., Teor. Verojatnost. i Primenen. 13 (1968), 631–641 (Russian, with English summary). MR 0243571 (39 #4892)
  • 2. V. F. Kolchin, Sluchainye grafy, \cyr Teoriya Veroyatnosteĭ\ i Matematicheskaya Statistika. [Probability Theory and Mathematical Statistics], Fiziko-Matematicheskaya Literatura, Moscow, 2000 (Russian, with Russian summary). 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), http://dx.doi.org/10.1515/rose.1993.1.2.171
  • 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, Kurs teorii veroyatnostei i matematicheskoi statistiki, “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: http://dx.doi.org/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): December 27, 2005
Published electronically: July 14, 2008
Article copyright: © Copyright 2008 American Mathematical Society