Highly dense mobile networks with random fadings
  Master thesis at TU Berlin with Wolfgang K\"{o}nig, April 2016.   We investigate a wireless network where the users are located according to a Poisson point process in a bounded subset of R^d, in the high-density limit. Assuming that the users have i.i.d. random fadings, interpreted as their loudnesses, we describe the large deviation properties of rare frustration events. This provides a variational formula, which we analyze in more detail, in order to describe the most likely settings with unusually many users who experience bad connection. We also compare effects coming from the random spatial positions of the users with effects coming from the random fadings.   Keywords: wireless communication, relaying, random fadings, high-density limit, large deviations, discretization, frustration probabilities, minimizers of relative entropy, average loudness. 
Andr\'as J\'ozsef T\'obi\'as
math.PR