Abstract Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies a higher scale level is used. Versions of proposed take seriously avoid assignment artificial scores. The construction principle based on an investigation binary models implicitly used in parametric regression. These building blocks can be fitted by combined similar...

In a recent paper Broutin and Devroye (2005) have studied the height of a class of edge-weighted random trees. This is a class of trees growing in continuous time which includes many well known trees as examples. In this paper we derive a limit theorem for the internal path length for this class of trees. The application of this limit theorem to concrete examples depends upon the possibility to...

The Wiener index is analyzed for random recursive trees and random binary search trees in the uniform probabilistic models. We obtain the expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed-point equations. Covariances, asymptotic correlations, and bivariate ...

We study the number of subtrees on the fringe of random recursive trees and random binary search trees whose limit law is known to be either normal or Poisson or degenerate depending on the size of the subtree. We introduce a new approach to this problem which helps us to further clarify this phenomenon. More precisely, we derive optimal Berry-Esseen bounds and local limit theorems for the norm...

Exponential bounds and tail estimates are derived for additive random recursive sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise as parameters of divide and conquer type algorithms. We derive tail bounds from estimates of the Laplace transforms and of the moment sequences. For the proof we use some clas...

Given a set S of n ≥ d points in general position in Rd, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree is a binary space partition tree obtained by recursive application of random hyperplane splits. We investigate the structural distributions of such random trees...

The \(k\)-cut number of rooted graphs was introduced by Cai et al. as a generalization the classical cutting model Meir and Moon. In this paper, we show that all moments conditioned Galton-Watson trees converge after proper rescaling, which implies convergence in distribution to same limit law regardless offspring trees. This extends result Janson. Using method, also various random or determini...