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DTSTAMP:20260407T051551Z
UID:64b9491b15a88591585873@ist.ac.at
DTSTART:20240528T163000
DTEND:20240528T173000
DESCRIPTION:Speaker: Lorenzo Dello Schiavo\nhosted by Jan Maas\nAbstract: L
 et W be a conservative\, ergodic Markov diffusion on some arbitrary state 
 space M\, converging exponentially fast to equilibrium. We consider: (1) S
 ystems of up to countably many massive particles in M\, with finite total 
 mass. Each particle is subject to an independent instance of the noise W\,
  with volatility the inverse mass carried by the particle. We prove that t
 he corresponding infinite system of SDEs has a unique solution\, for every
  starting configuration and every distribution of the masses in the infini
 te simplex. (2) Solutions to the Dean--Kawasaki SPDE with singular drift\,
  driven by the generator L of W. We prove that the equation may be given r
 igorous meaning on M\, and that it has a unique distributional solution. T
 his extends Konarovskyi--Lehmann--von Renesse's ill-posedness vs. triviali
 ty' to the case of infinitely many massive particles.(3) Diffusions with v
 alues in the space P of all probability measures on M\, driven by the geom
 etry induced by L.(4) In the case when M is a manifold\, differential-geom
 etric and metric-measure Brownian motions on P induced by the geometry of 
 optimal transportation and reversible for a normalized completely random m
 easure.We show that all these objects coincide.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Lorenzo Dello Schiavo: Massive Particle Systems\, Wasserstein Brown
 ian Motions\, and the Dean--Kawasaki SPDE
URL:https://talks-calendar.ista.ac.at/events/4973
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