Correlated randomness: Some examples of exotic statistical physics

One challenge of biology, medicine, and economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture - crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time and remarkably fine-tuned structures in space. To understand this 'miracle', one might consider placing aside the human tendency to see the universe as a machine. Instead, one might address the challenge of uncovering how, through randomness (albeit, as we shall see, strongly correlated randomness), one can arrive at many spatial and temporal patterns in biology, medicine, and economics. Inspired by principles developed by statistical physics over the past 50 years - scale invariance and universality - we review some recent applications of correlated randomness to fields that might startle Boltzmann if he were alive today.