A multivariate Poisson theorem for the number of solutions close to given vectors of a system of random linear equations
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V. A. Kopyttsev
We consider the number ξ(A, b | z) of solutions of a system of random linear equations Ax = b over a finite field K which belong to the set Xr(z) of the vectors differing from a given vector z in a given number r of coordinates (or in at most a given number of coordinates). We give conditions under which, as the number of unknowns, the number of equations, and the number of noncoinciding coordinates tend to infinity, the limit distribution of the vector (ξ(A, b | z(1)), …, ξ(A, b | z(k))) (or of the vector obtained from this vector by normalisation or by shifting some components by one) is the k-variate Poisson law. As corollaries we get limit distributions of the variable (ξ(A, b | z(1), …, z(k)) equal to the number of solutions of the system belonging to the union of the sets Xr(z(s)), s = 1, …, k. This research continues a series of the author's and V. G. Mikhailov's studies.
© de Gruyter
Articles in the same Issue
- Properties of the output sequence of a simplest 2-linear shift register over Z2n
- A multivariate Poisson theorem for the number of solutions close to given vectors of a system of random linear equations
- Critical multitype branching processes in a random environment
- On the intersection number of a graph
- Generalised Pascal pyramids and their reciprocals
- On identical transformations in commutative semigroups
Articles in the same Issue
- Properties of the output sequence of a simplest 2-linear shift register over Z2n
- A multivariate Poisson theorem for the number of solutions close to given vectors of a system of random linear equations
- Critical multitype branching processes in a random environment
- On the intersection number of a graph
- Generalised Pascal pyramids and their reciprocals
- On identical transformations in commutative semigroups
