This story yesterday (no need to follow the link to understand the question!)
reminds me that I've often wondered about the following:
Suppose you have a fixed mortality curve $f(x)$ expressing the probability of a person's remaining alive at age $x$. Suppose also, for simplicity, you have a steady state population, so a given fixed birth rate. How would one compute from $f(x)$, and the birth rate, the probability distribution $\rho$ governing the time intervals from one "world's oldest person dies" event to the next?
Actually though I think I could probably write down explicit integrals to answer my own question literally, but I don't expect they would say much as such. So I'm really looking for a softer answer that would explain what features of $f(x)$, what measures of the heaviness of its tail I guess, dominate the behavior of $\rho$ and how?