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SUMMARY:Size-biased diffusion limits and the inclusion process - Stefan Gr
osskinsky (Augsburg)
DTSTART;VALUE=DATE-TIME:20240304T140000Z
DTEND;VALUE=DATE-TIME:20240304T150000Z
UID:https://talks.ox.ac.uk/talks/id/3ed6dc09-3d91-48ef-a6a0-b81f289198a3/
DESCRIPTION:We study the Inclusion Process with vanishing diffusion coeffi
cient\, which is a stochastic particle system known to exhibit condensatio
n and metastable dynamics for cluster locations. We focus on the dynamics
of the empirical mass distribution and consider the process on the complet
e graph in the thermodynamic limit with fixed particle density. Describing
a given configuration by a measure on a suitably scaled mass space\, we e
stablish convergence to a limiting measure-valued process. When the diffus
ion coefficient scales like the inverse of the system size\, the scaling l
imit is equivalent to the well known Poisson-Dirichlet diffusion. Our appr
oach can be generalized to other scaling regimes\, providing a natural ext
ension of the Poisson-Dirichlet diffusion to infinite mutation rate. Consi
dering size-biased mass distributions\, our approach yields an interesting
characterization of the limiting dynamics via duality.\nThis is joint wor
k with Simon Gabriel (Münster) and Paul Chleboun (both Warwick).\nSpeaker
s:\nStefan Grosskinsky (Augsburg)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/3ed6dc09-3d91-48ef-a6a0-b81f289198a3/
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DESCRIPTION:Talk:Size-biased diffusion limits and the inclusion process -
Stefan Grosskinsky (Augsburg)
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