In this talk, I will present new asymptotic upper bounds on the transport capacity of both one-dimensional and two-dimensional random ad hoc wireless networks. The results we obtain are of information theoretic nature, in the sense that we do not make any assumption on the way communication takes place in the network. Our approach leads us to the study of determinants of Cauchy matrices, which I will detail carefully during the talk.
This is joint work with Emmanuel Preissmann and Ayfer Ozgur at EPFL.