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SUMMARY:Scaling limit of a branching process in a varying environment - Gu
 illaume Conchon-Kerjan (Bath)
DTSTART:20221018T130000Z
DTEND:20221018T140000Z
UID:TALK183188@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:A branching process in varying environment is a Galton-Watson 
 tree whose offspring distribution can change at each generation. The evolu
 tion of the size of successive generations has drawn a lot of attention in
  recent years\, both from the discrete and continuum points of view (the s
 caling limit being a modified Continuous State Branching Process).\nWe foc
 us on the limiting genealogical structure\, which is more delicate to stud
 y. In the critical case (all distributions have offspring mean 1)\, we sho
 w that under mild second moment assumptions on the sequence of offspring d
 istributions\, a BPVE conditioned to be large converges to the Brownian Co
 ntinuum Random Tree\, as in the standard Galton-Watson setting. The varyin
 g environment adds asymmetry and dependencies in many places. This require
 s numerous changes to the usual arguments. In particular we employ a (to o
 ur knowledge) new connexion between the Łukasiewicz path and the height p
 rocess.\nThis is a joint work with Daniel Kious and Cécile Mailler.
LOCATION:MR12\, Centre for Mathematical Sciences
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