BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Asymptotic behaviour of near-critical branching Brownian motion - 
 Nathanaël Berestycki (Cambridge)
DTSTART:20100504T153000Z
DTEND:20100504T163000Z
UID:TALK24733@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Consider a system of particles that perform branching Brownian
  motion with negative drift \\sqrt(2- \\eps) and are killed upon hitting z
 ero. Initially\, there is just one particle at x. Kesten (1978) proved tha
 t the system survives if and only if \\eps>0. In this talk I shall describ
 e recent joint work with Julien Berestycki and Jason Schweinsberg concerni
 ng the limiting behaviour of this process as \\eps tends to 0. In particul
 ar we establish sharp asymptotics for the limiting survival probability as
  a function of the starting point x. Moreover\, the limiting genealogy bet
 ween individuals from this population is shown to have a characteristic ti
 me scale of order \\eps^{-3/2}. When time is measured in these units we sh
 ow that the geometry of the genealogical tree converges to the Bolthausen-
 Sznitman coalescent. This is closely related to a set of conjectures by Br
 unet\, Derrida and Simon. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
END:VEVENT
END:VCALENDAR