# Power-law distribution from superposition of exponential distributions

In the previous post we have asked a simple question - what if gap duration is distributed according to a power-law distribution. Our answer was an apparently pure 1/f noise. But how could the power-law distribution arise? While in some materials some quantities indeed follow power-law distribution (such as blinking times in quantum dot experiments [1]), most materials have exponentially distributed generation and/or recombination times. So then, can we construct a power-law distribution from superposition of exponential distributions?