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We consider the power efficiency of a communications channel, i.e., the maximum bit rate that can be achieved per unit power (energy rate). For additive white Gaussian noise (AWGN) channels, it is well known that power efficiency is attained in the low signal-to-noise ratio (SNR) regime where capacity is proportional to the transmit power. In this paper, we first show that for a random sensory wireless network with n users (nodes) placed in a domain of fixed area, with probability converging to one as n grows, the power efficiency scales at least by a factor of √n. In other words, each user in a wireless channel with n nodes can support the same communication rate as a single-user system, but by expending only 1/√n times the energy. Then we look at a random ad hoc network with n relay nodes and r simultaneous transmitter/receiver pairs located in a domain of fixed area. We show that as long as r≤√n, we can achieve a power efficiency that scales by a factor of √n. We also give a description of how to achieve these gains.