Coalescing times for IID random variables with applications to population biology

We consider a coalescing particle model where particles move in discrete time. At each time period, each remaining ball is independently put in one of n bins according to a probability distribution p ( p1, . . . , pn), and all balls put into the same bin merge into a single ball. Starting with k balls, we are interested in the properties of E[N(p, k)], the expected time until all balls merge into one. We derive both upper and lower bounds for E[N(p, k)], some asymptotic results, and show that P{N(p, k) t}, and thus E[N(p, k)], is a Schur concave function of p. Applications to population biology are noted. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 155–166, 2003