Sufficient conditions for asymptotic normality of number of multiple repetitions of chains in marked complete trees and forests

Abstract

We consider complete q-ary trees of height H with vertices marked by random independent marks taking values from the set {1,2,...,N} and forests of such trees. For both cases we investigate the number of sets of r ≥ 2 paths with fixed length s such that corresponding s-chains of marks of vertices are identical. We propose three theorems on sufficient conditions for the asymptotic normality for considered random values as H → ∞ and possibly varying parameters s and q