An estimate for the rate of convergence of the distribution of the number of false solutions of a system of nonlinear random equations in the field
Authors:
V. I. Masol and M. V. Slobodyan
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal:
Theor. Probability and Math. Statist. 77 (2008), 121134
MSC (2000):
Primary 60C05, 15A52, 15A03
Published electronically:
January 16, 2009
Fulltext PDF Free Access
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Abstract: We prove a result on the rate of convergence as of the distribution of the number of false solutions of a system of nonlinear random equations in the field to the Poisson distribution with parameter . We assume, in particular, that the difference between the number of unknowns and the number of equations of the system is a constant .
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I. Masol, A theorem on the limit distribution of the number of
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41–56 (Russian, with Russian summary); English transl., Theory
Probab. Appl. 43 (1999), no. 1, 75–88. MR 1669972
(2000f:60040), http://dx.doi.org/10.1137/S0040585X97976672
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 V. I. Masol, A theorem on the limit distribution of the number of false solutions of a system of nonlinear random Boolean equations, Teor. Veroyatnost. i Primenen. 43 (1998), no. 1, 4156; English transl. in Theory Probab. Appl. 43 (1999), no. 1, 7588. MR 1669972 (2000f:60040)
 2.
 W. Feller, An Introduction to Probability Theory and its Applications, 3rd ed., vol. I, John Wiley & Sons, New YorkLondonSydney, 1968. MR 0228020 (37:3604)
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 V. N. Sachkov, Introduction to Combinatorial Methods of Discrete Mathematics, ``Nauka'', Moscow, 1982. (Russian) MR 700691 (85g:05001)
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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
M. V. Slobodyan
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:
mslob@ukr.net
DOI:
http://dx.doi.org/10.1090/S0094900009007510
PII:
S 00949000(09)007510
Keywords:
System of nonlinear random equations,
the field $GF(2)$,
rate of convergence
Received by editor(s):
February 10, 2006
Published electronically:
January 16, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
