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SUMMARY:Limit distributions of branching Markov chains - Vadim Kaimanovich
(Ottawa)
DTSTART;VALUE=DATE-TIME:20220304T120000Z
DTEND;VALUE=DATE-TIME:20220304T130000Z
UID:https://talks.ox.ac.uk/talks/id/dd2b1d39-cb55-4599-a90f-b36edd6c1cae/
DESCRIPTION:The talk is based on joint work with Wolfgang Woess. There is
a large body\nof literature devoted to the quantitative aspects of branchi
ng random\nwalks on the additive group of real numbers and to the behaviou
r of the\nassociated martingales. In what concerns more general state spac
es rich\nenough to have a non-trivial topological boundary at infinity (li
ke\, for\ninstance\, infinite trees)\, it is natural to ask about the limi
t behaviour\nof the branching populations in geometric terms. Non-trivial
limit sets of\nrandom population sequences were first exhibited by Liggett
(1996) and\nlater studied in similar situations by Hueter - Lalley (2000)
\, Benjamini -\nMuller (2012)\, \nCandellero – Roberts (2015) and Hutchc
roft (2020).\n\nWe are looking at branching random walks from a different
and apparently\nnovel angle. We are interested in the random limit boundar
y measures\narising from the uniform distributions on sample populations.
Unlike with\nthe limit sets\, the very existence of the limit measures is
already a\nnon-trivial problem. We consider and solve this problem in two
different\nsetups: in the topological one (when the boundary of the state
space is\nprovided by a certain compactification) and in the measure-theor
etical one\n(when we are dealing with the Poisson or exit boundary of the
underlying\nMarkov chain on the state space).\nSpeakers:\nVadim Kaimanovic
h (Ottawa)
LOCATION:Mathematical Institute\, L4
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/dd2b1d39-cb55-4599-a90f-b36edd6c1cae/
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DESCRIPTION:Talk:Limit distributions of branching Markov chains - Vadim Ka
imanovich (Ottawa)
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