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SUMMARY:Yaglom-type limit theorems for branching Brownian motion with abso
 rption - Jason Schweinsberg (University of California\, San Diego)
DTSTART:20180713T133500Z
DTEND:20180713T142000Z
UID:TALK108076@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We consider one-dimensional branching Brownian motion in which
  particles are&nbsp\;absorbed at the origin. We assume that when a particl
 e branches\, the offspring&nbsp\;distribution is supercritical\, but the p
 articles are given a critical drift towards the&nbsp\;origin so that the p
 rocess eventually goes extinct with probability one. We&nbsp\;establish pr
 ecise asymptotics for the probability that the process survives for a&nbsp
 \;large time t\, improving upon a result of Kesten (1978) and Berestycki\,
 &nbsp\;Berestycki\, and Schweinsberg (2014). We also prove a Yaglom-type l
 imit&nbsp\;theorem for the behavior of the process conditioned to survive 
 for an unusually&nbsp\;long time\, which also improves upon results of Kes
 ten (1978). An important tool&nbsp\;in the proofs of these results is the 
 convergence of branching Brownian motion&nbsp\;with absorption to a contin
 uous state branching process.<br><br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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