Estimates for the probability that a system of random equations is solvable in a given set of vectors over the field GF(3). (English. Ukrainian original) Zbl 1333.60066
Theory Probab. Math. Stat. 87, 135-152 (2013); translation from Teor. Jmovirn. Mat. Stat. 87, 120-135 (2012).
Summary: Let \(P_n\) be the probability that a second order system of nonlinear random equations over the field \(\mathrm{GF}(3)\) 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.
MSC:
| 60F99 | Limit theorems in probability theory |
| 12E12 | Equations in general fields |
| 12E20 | Finite fields (field-theoretic aspects) |
Keywords:
nonlinear random equations; probability of solvability; rate of convergence; three-elemental fieldReferences:
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