Conditions for exchangeable coalescents to come down from infinity
نویسنده
چکیده
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, 1–50.
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