Henning Sulzbach

On a functional contraction method

Methods for proving functional limit laws are developed for sequences of stochastic processes which allow a recursive distributional decomposition either in time or space. Our approach is an extension of the so-called contraction method to the space C[0,1] of continuous functions endowed with uniform topology and the space D[0,1] of cadlag functions with the Skorokhod topology. The contraction method originated from the probabilistic analysis of algorithms and random trees where characteristics satisfy natural distributional recurrences. It is based on stochastic fixed-point equations, where probability metrics can be used to obtain contraction properties and allow the application of Banach’s fixed-point theorem. We develop the use of the Zolotarev metrics on the spaces C[0,1] and D[0,1] in this context. Applications are given, in particular, a short proof of Donsker’s functional limit theorem is derived and recurrences arising in the probabilistic analysis of algorithms are discussed.

Partial match queries in random quadtrees

We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the traditional model where the data consist of independent and uniform points in the unit square. For this model, in a structure on

The dual tree of a recursive triangulation of the disk

n

On martingale tail sums in affine two-color urn models with multiple drawings

points, it is known that the number of nodes

General Edgeworth expansions with applications to profiles of random trees

C_n(\xi)

On Weighted Depths in Random Binary Search Trees

to visit in order to report the items matching an independent and uniformly on

Refined Asymptotics for the Number of Leaves of Random Point Quadtrees

[0,1]

A limit process for partial match queries in random quadtrees and

random query

2

\xi

-d trees

satisfies