On Spectrum and Infrastructure Sharing in Multi-Operator Cellular   Networks
  In this paper, we introduce a mathematical framework for analyzing and optimizing multi-operator cellular networks that are allowed to share spectrum licenses and infrastructure elements. The proposed approach exploits stochastic geometry for modeling the locations of cellular base stations and for computing the aggregate average rate. The trade-offs that emerge from sharing spectrum frequencies and cellular base stations are quantified and discussed. 
Shanshan Wang, Konstantinos Samdanis, Xavier Costa Perez, and Marco Di   Renzo
cs.IT math.IT