  We propose a new class of algorithms for randomly scheduling network
transmissions. The idea is to use (discrete) determinantal point processes
(subsets) to randomly assign medium access to various {\em repulsive} subsets
of potential transmitters. This approach can be seen as a natural extension of
(spatial) Aloha, which schedules transmissions independently. Under a general
path loss model and Rayleigh fading, we show that, similarly to Aloha, they are
also subject to elegant analysis of the coverage probabilities and transmission
attempts (also known as local delay). This is mainly due to the explicit,
determinantal form of the conditional (Palm) distribution and closed-form
expressions for the Laplace functional of determinantal processes.
Interestingly, the derived performance characteristics of the network are
amenable to various optimizations of the scheduling parameters, which are
determinantal kernels, allowing the use of techniques developed for statistical
learning with determinantal processes. Well-established sampling algorithms for
determinantal processes can be used to cope with implementation issues, which
is is beyond the scope of this paper, but it creates paths for further
research.
