On a coalescence process and its branching genealogy
arXiv:1709.07633 · doi:10.1017/jpr.2016.71
Abstract
We define and analyze a coalescent process as a recursive box-filling process whose genealogy is given by an ancestral time-reversed, time-inhomogeneous Bienyamé-Galton-Watson process. Special interest is on the expected size of a typical box and its probability of being empty. Special cases leading to exact asymptotic computations are investigated when the coalescing mechanisms are either linear-fractional or quadratic.
10 pages, one figure