![]() ![]() ![]() We give explicit formulas for the distribution of the coalescent times, as well as a construction of the genealogical tree involving a mixture of independent and identically distributed random variables. The randomly fluctuating population size, as opposed to constant size populations where the Kingman coalescent more usually arises, have a pronounced effect on both the results and the method of proof required. Viewed backwards in time, the resulting coalescent process is topologically equivalent to Kingman's coalescent, but the times of coalescence have an interesting and highly nontrivial structure. What does the ancestral tree drawn out by these k particles look like? Some special cases are known but we give a more complete answer.We concentrate on near-critical cases where the mean number of offspring is 1 + μ/T for some μ ∈ R, and show that a scaling limit exists as T →∞. If the system survives until a large time T, then choose k particles uniformly from those alive. N2 - Take a continuous-time Galton-Watson tree. © Institute of Mathematical Statistics, 2020. Johnston was supported during for the major part of this work by University of Bath URS funding. Roberts was supported during the early stages of this work by EPSRC fellowship EP/K007440/1, and during the latter stages by a Royal Society University Research Fellowship. T1 - The coalescent structure of continuous-time Galton-Watson trees In general subcritical and supercritical cases it is not possible to give such explicit formulas, but we highlight the special case of birth-death processes.", In general subcritical and supercritical cases it is not possible to give such explicit formulas, but we highlight the special case of birth-death processes.Ībstract = "Take a continuous-time Galton-Watson tree. ![]() Take a continuous-time Galton-Watson tree. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |