We investigate the dynamics of a class of recurrent random networks with sparse, asymmetric excitatory connectivity and global shunting inhibition mediated by a single interneuron. Using probabilistic arguments and a hyperbolic tangent approximation to the gaussian, we develop a simple method for setting the average level of firing activity in these networks. We demonstrate through simulations that our technique works well and extends to networks with more complicated inhibitory schemes. We are interested primarily in the CA3 region of the mammalian hippocampus, and the random networks investigated here are seen as modeling the a priori dynamics of activity in this region. In the presence of external stimuli, a suitable synaptic modification rule could shape this dynamics to perform temporal information processing tasks such as sequence completion and prediction.