A diffuser traversing an infinitely steep ‘potential slide’ might never overcome it. In such cases, the notion of First Passage Time—‘how long would it take till the diffuser surmounts the slide?’—is inadequate. Rather, the notion of relevance is that of Peak Height—‘how high-up...

We consider an evolving ensemble assembled from a set of n different elements via a stochastic growth process in which independent and identically distributed copies of the elements arrive randomly in time, and their statistics are governed by Zipf’s law. The associated “Heaps process” is...