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Λ-coalescents: a survey

Part of: Markov processes Stochastic processes Combinatorial probability

Published online by Cambridge University Press:  30 March 2016

Alexander Gnedin ,
Alexander Iksanov  and
Alexander Marynych
Alexander Gnedin
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK. Email address: a.gnedin@qmul.ac.uk.
Alexander Iksanov
Affiliation:
Faculty of Cybernetics, National Taras Shevchenko University of Kiev, 01033 Kiev, Ukraine. Email address: iksan@univ.kiev.ua.
Alexander Marynych
Affiliation:
Faculty of Cybernetics, National Taras Shevchenko University of Kiev, 01033 Kiev, Ukraine. Email address: marynych@unicyb.kiev.ua.
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Abstract

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Λ-coalescents model the evolution of a coalescing system in which any number of components randomly sampled from the whole may merge into larger blocks. This survey focuses on related combinatorial constructions and the large-sample behaviour of the functionals which characterize in some way the speed of coalescence.

Keywords

Coalescent with multiple mergersexchangeable partitionslarge-sample asymptotics

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60C05: Combinatorial probability 60G09: Exchangeability 60G51: Processes with independent increments; L'evy processes
Type
Part 2. The 2014 AP lectures
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 23 - 40
Copyright
Copyright © Applied Probability Trust 2014 

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