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Theory of Probability and Mathematical Statistics

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Estimates for the probability that a system of random equations is solvable in a given set of vectors over the field $ {GF}(3)$


Authors: V. I. Masol and L. O. Romashova
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 135-152
DOI: https://doi.org/10.1090/S0094-9000-2014-00909-6
Published electronically: March 21, 2014
MathSciNet review: 3241451
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Abstract | References | Additional Information

Abstract: Let $ P_n$ be the probability that a second order system of nonlinear random equations over the field $ \text {\bf {GF}}(3)$ has a solution in a given set of vectors, where $ n$ is the number of unknowns in the system. A necessary and sufficient condition is found for $ P_n\to 0$ as $ n\to \infty $. Some rates of convergence to zero are found and some applications are described.


References [Enhancements On Off] (What's this?)

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Additional Information

V. I. Masol
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine

L. O. Romashova
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: deezee@ukr.net

DOI: https://doi.org/10.1090/S0094-9000-2014-00909-6
Keywords: System of nonlinear random equations, probability that a system is solvable, rate of convergence, a field containing three elements
Received by editor(s): July 4, 2011
Published electronically: March 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society

American Mathematical Society