Conditions for exchangeable coalescents to come down from infinity. (English) Zbl 1277.60122

Herriger, Philip; Möhle, Martin

ALEA, Lat. Am. J. Probab. Math. Stat. 9, No. 2, 637-665 (2012).

Summary: An improved condition to come down from infinity for exchangeable coalescent processes with simultaneous multiple collisions of ancestral lineages is provided. For non-critical coalescents this leads to an improved necessary and sufficient condition for the coalescent to come down from infinity. An analog conjecture for the full class of exchangeable coalescents is presented. New examples of critical coalescents are studied in detail. The results extend those obtained by J. Schweinsberg in Section 5.5 of [“Coalescents with simultaneous multiple collisions”, Electron. J. Probab. 5, Paper No. 12, 50 p. (2000; Zbl 0959.60065)].

MSC:

60J25	Continuous-time Markov processes on general state spaces
60G09	Exchangeability for stochastic processes
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
60J75	Jump processes (MSC2010)
05A18	Partitions of sets
92D15	Problems related to evolution

Keywords:

absorption time; coming down from infinity; exchangeable coalescent; simultaneous multiple collisions

Citations:

Zbl 0959.60065