Toronto Probability Seminar
Mondays, 4-5, Fields
Institute Library
University of Toronto
campus
222 College Street (see
FI in map)
Tuesday, April 14, 2008, 10:00pm
B6183, Bahen buillding
Nathanael Berestycki
(University of Cambridge)
The speed of coming down from infinity for coalescent processes
I will talk about some joint work with J. Berestycki and V. Limic
regarding coalescent processes with multiple collisions. These processes
describe the mean-field aggregation of exchangeable and massless
particles, when several particles can merge together at any given time.
It is known that some of these processes can come down from infinity,
meaning that even though initially there are infinitely many particles,
after any given positive amount of time, the number of particles has
become finite a.s. We show a connection to branching processes and
continuous random trees, which allows us to analyze the exact speed at
which this phenomenon occurs, meaning at what rate the number of
particles diverges to inifinity asymptotically near time zero, as well
as characterize the measures Lambda for which this phenomenon occurs,
recovering an earlier criterion due to J. Schweinsberg. This turns out
to have a number of applications, in particular to population genetics,
which I will also try to describe if time permits.
(Click
here for past talks)
Upcoming talks
Organizers
Bálint Virág
,
Benedek Valkó
University of Toronto, Mathematics and Statistics
For questions, scheduling, or to be added to the mailing list, contact the organizers at
probsem-at-math-dot-toronto-dot-edu,