On Additive Functionals

Additive functionals on multiway search trees

We derive asymptotics of moments and limiting distributions, under the random permutation model on m-ary search trees on n keys, of functionals that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal path length, and the socalled shape functional fall under this framework. The limiting behavior of these functionals exhibi...

Limiting distributions for additive functionals on Catalan trees

Additive tree functionals represent the cost of many divide-andconquer algorithms. We derive the limiting distribution of the additive functionals induced by toll functions of the form (a) nα when α > 0 and (b) log n (the so-called shape functional) on uniformly distributed binary search trees, sometimes called Catalan trees. The Gaussian law obtained in the latter case complements the central ...

Additive functionals on spaces with non-absolutely-continuous norm

Additive Functionals of Infinite-variance Moving Averages

We consider the asymptotic behavior of additive functionals of linear processes with infinite variance innovations. Applying the central limit theory for Markov chains, we establish asymptotic normality for short-range dependent processes. A non-central limit theorem is obtained when the processes are long-range dependent and the innovations are in the domain of attraction of stable laws.

Characterizing neuromorphologic alterations with additive shape functionals

The complexity of a neuronal cell shape is known to be related to its function. Specifically, among other indicators, a decreased complexity in the dendritic trees of cortical pyramidal neurons has been associated with mental retardation. In this paper we develop a procedure to address the characterization of morphological changes induced in cultured neurons by over-expressing a gene involved i...