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SUMMARY: Selection principles for the N-BBM and the Fleming-Viot particle
system - Oliver Tough (University of Bath)
DTSTART;VALUE=DATE-TIME:20231127T140000Z
DTEND;VALUE=DATE-TIME:20231127T150000Z
UID:https://talks.ox.ac.uk/talks/id/cf7ab8cd-cb8b-45f2-a185-be98176e2e78/
DESCRIPTION:The selection problem is to show\, for a given branching parti
cle system with selection\, that the stationary distribution for a large b
ut finite number of particles corresponds to the travelling wave of the as
sociated PDE with minimal wave speed. This had been an open problem for an
y such particle system.\nThe N-branching Brownian motion with selection (N
-BBM) is a particle system consisting of N independent particles that diff
use as Brownian motions in $\\mathbb{R}$\, branch at rate one\, and whose
size is kept constant by removing the leftmost particle at each branching
event. We establish the following selection principle: as $N\\rightarrow\\
infty$ the stationary empirical measure of the $N$-particle system converg
es to the minimal travelling wave of the associated free boundary PDE. Mor
eover we will establish a similar selection principle for the related Flem
ing-Viot particle system with drift $-1$\, a selection problem which had a
risen in a different context.\nWe will discuss these selection principles\
, their backgrounds\, and (time permitting) some of the ideas introduced t
o prove them.\nThis is based on joint work with Julien Berestycki.\nSpeake
rs:\nOliver Tough (University of Bath)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/cf7ab8cd-cb8b-45f2-a185-be98176e2e78/
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DESCRIPTION:Talk: Selection principles for the N-BBM and the Fleming-Viot
particle system - Oliver Tough (University of Bath)
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