In this paper, we study physical layer security for the downlink of cellular networks, where the confidential messages transmitted to each mobile user can be eavesdropped by both; 1) the other users in the same cell and 2) the users in the other cells. The locations of base stations and mobile users are modeled as two independent two-dimensional Poisson point processes. Using the proposed model, we analyze 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 approximations for the probability of secrecy outage and the mean secrecy rate, and characterize regimes where RCI precoding achieves a non-zero secrecy rate. We find that unlike isolated cells, if one treats interference as noise, the secrecy rate in a cellular network does not grow monotonically with the transmit power, and the network tends to be in secrecy outage if the transmit power grows unbounded. Furthermore, we show that there is an optimal value for the base station deployment density that maximizes the secrecy rate, and this value is a decreasing function of the transmit power.