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UID:www.tcs.tifr.res.in/event/1200
DTSTAMP:20230914T125954Z
SUMMARY:Power-laws and weak convergence of the Kingman coalescent
DESCRIPTION:Speaker: Henrik Hult (KTH Royal Institute of Technology)\n\nAbs
 tract: \nThe Kingman coalescent is an important and well-studied process i
 n population genetics modelling the ancestry of a sample of individuals. I
 n this talk weak convergence results are presented that characterise asymp
 totic properties of the Kingman coalescent under parent dependent mutation
 s\, as the sample size grows to infinity. It is shown that the sampling pr
 obability satisfies a power-law and we derive the asymptotic behaviour of 
 transition probabilities of the block counting jump chain. For the normali
 sed jump chain and number of mutations between types a limiting process is
  derived consisting of a deterministic component\, describing the limit of
  the block counting jump chain\, and independent Poisson processes with st
 ate-dependent intensities\, exploding at the origin\, describing the limit
  of the number of mutations. Finally\, the results are extended to charact
 erise the asymptotic performance of popular importance sampling algorithms
 \, such as the Griffiths-Tavare algorithm and the Stephens-Donnelly algori
 thm. This is joint work with Martina Favero.\n
URL:https://www.tcs.tifr.res.in/web/events/1200
DTSTART;TZID=Asia/Kolkata:20220429T160000
DTEND;TZID=Asia/Kolkata:20220429T170000
LOCATION:A-201 Seminar Room
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