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), 121-134

MSC (2000):
Primary 60C05, 15A52, 15A03

DOI:
https://doi.org/10.1090/S0094-9000-09-00751-0

Published electronically:
January 16, 2009

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Abstract | References | Similar Articles | Additional Information

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 .

**1.**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, 41–56 (Russian, with Russian summary); English transl., Theory Probab. Appl.**43**(1999), no. 1, 75–88. MR**1669972**, https://doi.org/10.1137/S0040585X97976672**2.**William Feller,*An introduction to probability theory and its applications. Vol. I*, Third edition, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR**0228020****3.**V. N. Sachkov,*\cyr Vvedenie v kombinatornye metody diskretnoĭ matematiki*, “Nauka”, Moscow, 1982 (Russian). MR**700691**

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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:
https://doi.org/10.1090/S0094-9000-09-00751-0

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