  We provide closed-form approximations to the performance gain achieved in a
RIS-assisted communication. We then consider a network deployment of RIS and
Transmitter-Receiver pairs and use these approximate expressions to provide
equivalence models which state that the performance of a RIS-equipped network
is similar to the performance of an appropriately spatially scaled system. We
provide a way of assigning available RIS to assist communication between
several transmitter-receiver pairs. Several such approximations are expected to
spawn from this study, with more clarity on structural aspects of the gains
achieved in RIS-assisted communications.
