Multivariate normal limit laws for the numbers of fringe subtrees in m-ary search trees and preferential attachment trees
2017
Abstract
We study fringe subtrees of random m-ary search trees and of preferential attachment trees, by putting them in the context of generalised Polya urns. In particularwe show that for the random m-ary search trees with m<=26 and for the linear preferential attachment trees, the number of fringe subtrees that are isomorphic to an arbitrary fixed tree T converges to a normal distribution; more generally, we also prove multivariate normal distribution results for random vectors of such numbers for different fringe subtrees.
Furthermore, we show that the number of protected nodes in random m-ary search trees for m<=26 has asymptotically a normal distribution.