V. G. Mikhailov
Limit theorems for the number of points of a given set covered by a random linear subspace
Let V T
be the T -dimensional linear space over a finite field K, and let B
1,..., B
m be subsets of VT
not containing the zero-point. Let a subspace L be chosen randomly and equiprobably
from the set of all n-dimensional linear subspaces of VT
. We consider the number µ(Bi
) of points in the intersections L ∩ Bi
, i = 1,..., m. We study the limit behaviour of the distribution of the vector (µ(B1
),..., µ.(Bm
)) as T, n → ∞ and the sets vary in such a way that the means of µ(Bi
) tend to finite limits. The field K is fixed. We prove that this random vector has in limit the compound
Poisson distribution. Necessary and sufficient conditions for asymptotic independency of the random
variables µ(Bi
),...,µ(Bm
) are derived.
Discrete Mathematics and Applications, Walter de Gruyter
Print ISSN: 0924-9266
Volume: 13, 06/2003
Pages: 179 - 188
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