  In this paper, we consider the broadcast channel with confidential messages
and external eavesdroppers (BCCE), where a multi-antenna base station
simultaneously communicates to multiple potentially malicious users, in the
presence of randomly located external eavesdroppers. Using the proposed model,
we study the secrecy rates achievable by regularized channel inversion (RCI)
precoding by performing a large-system analysis that combines tools from
stochastic geometry and random matrix theory. We obtain explicit expressions
for the probability of secrecy outage and an upper bound on the rate loss due
to the presence of external eavesdroppers. We show that both these quantities
scale as $\frac{\lambda_e}{\sqrt{N}}$, where $N$ is the number of transmit
antennas and $\lambda_e$ is the density of external eavesdroppers, irrespective
of their collusion strategy. Furthermore, we derive a practical rule for the
choice of the regularization parameter, which is agnostic of channel state
information and location of eavesdroppers, and yet provides close to optimal
performance.
