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DTSTAMP:20261028T030753Z
SUMMARY:Stochastic Analysis Seminar – Matthias Erbar (Universität Bielef
 eld)
DESCRIPTION:Matthias Erbar\nTitle:\nOptimal transport and gradient flows fo
 r point processes\nAbstract\n\n\n\nI will describe a theory of optimal tra
 nsport for stationary random measures with a focus on stationary point pro
 cesses. We consider two types of distances on stationary probability measu
 res on the configuration space geared towards different dynamics of point 
 configurations. The first one is based on continuous displacement of point
 s and leads to a two layer optimal transport problem with a probabilistic 
 constraint. It gives rise to a natural notion of displacement interpolatio
 n between point processes and provides e.g. a characterisation of the evol
 ution of infinitely many (interacting) Brownian motions as the gradient fl
 ow of the specific free energy. The second notion is based on a birth-deat
 h dynamic of points and is modelled on the Benamou-Brenier formula. In a p
 erturbative regime around the Poisson process we obtain an EVI gradient fl
 ow characterisation of the associated Glauber dynamics. This is based on j
 oint work with Martin Huesmann\, Jonas Jalowy\, Bastian Müller\, and Hann
 a Stange.\n\n\n
URL:https://www.imperial.ac.uk/events/215834/stochastic-analysis-seminar-ma
 tthias-erbar-universitat-bielefeld/
DTSTART;TZID=Europe/London:20261103T150000
DTEND;TZID=Europe/London:20261103T160000
LOCATION:410\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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