  We motivate the study of a certain class of random Fibonacci sequences -
which we call continuous random Fibonacci sequences - by demonstrating that
their exponential growth rate can be used to establish capacity and power
scaling laws for multihop cooperative amplify-and-forward (AF) relay networks.
With these laws, we show that it is possible to construct multihop cooperative
AF networks that simultaneously avoid 1) exponential capacity decay and 2)
exponential transmit power growth across the network. This is achieved by
ensuring the network's Lyapunov exponent is zero.
