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), 135152
Published electronically:
March 21, 2014
MathSciNet review:
3241451
Fulltext 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:
http://dx.doi.org/10.1090/S009490002014009096
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
