Estimates for the probability that a system of random equations is solvable in a given set of vectors over the field

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

Full-text PDF

Abstract | References | Additional Information

Abstract: Let be the probability that a second order system of nonlinear random equations over the field has a solution in a given set of vectors, where is the number of unknowns in the system. A necessary and sufficient condition is found for as . Some rates of convergence to zero are found and some applications are described.

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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