Let V T be the T -dimensional linear space over a finite field K, and let B1,..., Bm 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.
Copyright 2003, Walter de Gruyter
