We give two new constructions of symmetric group divisible designs using divisible difference sets. These constructions generalize the McFarland and Spence constructions of symmetric designs. Divisible designs are of interest in several parts of mathematics: The design theorist needs classes of divisible designs as "ingredients" for recursive constructions of designs. Statisticians use divisibl...

We study the relation between stochastic domination of an innnitely divisible random vector X by another innnitely divisible random vector Y and their corresponding L evy measures. The results are used to derive a Slepian-type inequality for a general class of symmetric innnitely divisible random vectors.

Divisible load theory has become a popular area of research during the past two decades. Based on divisible load theory the computations and communications can be divided into some arbitrarily independent parts and each part can be processed independently by a processor. Existing divisible load scheduling algorithms do not consider any priority for allocating fraction of load. In some situation...

In a previous paper ([B-G1]), we defined the rectangular free convolution ⊞ λ . Here, we investigate the related notion of infinite divisibility, which happens to be closely related the classical infinite divisibility: there exists a bijection between the set of classical symmetric infinitely divisible distributions and the set of ⊞ λ -infinitely divisible distributions, which preserves limit t...

In this paper the equivalence between various divisible load-scheduling policies and continuous time Markov chains is demonstrated. This provides a basic unification of both data parallel divisible load scheduling and Markov chain models for the first time in 16 years of research. Such equivalence is demonstrated for divisible scheduling on linear daisy chains and single and two level tree netw...