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The time to absorption in Λ-coalescents

Published online by Cambridge University Press:  01 February 2019

Götz Kersting*
Affiliation:
Goethe University Frankfurt
Anton Wakolbinger*
Affiliation:
Goethe University Frankfurt
*
Institute of Mathematics, Goethe University Frankfurt, Robert Mayer Strasse 10, 60325 Frankfurt am Main, Germany. Email address: kersting@math.uni-frankfurt.de
Institute of Mathematics, Goethe University Frankfurt, Robert Mayer Strasse 10, 60325 Frankfurt am Main, Germany. Email address: wakolbinger@math.uni-frankfurt.de
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Abstract

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We present a law of large numbers and a central limit theorem for the time to absorption of Λ-coalescents with dust started from n blocks, as n→∞. The proofs rely on an approximation of the logarithm of the block-counting process by means of a drifted subordinator.

Type
Original Article
Copyright
Copyright © Applied Probability Trust 2018 

References

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