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Title	A partial Laplacian as an infinitesimal generator on the Wasserstein space
Creator	Gangbo, Wilfrid
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-04-10T10:32
Description	We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel probability measures, and we use it to define heat flow on the Wasserstein space. We verify a distinctive smoothing effect of this flow for a particular class of initial conditions. To this end, we will develop a theory of Fourier analysis and conic surfaces in metric spaces. We note that the use of the infinitesimal generators has been instrumental in proving various theorems for Mean Field Games, and we anticipate they will play a key role in future studies of viscosity solutions of PDEs in the Wasserstein space (Joint work with Y. T. Chow).
Extent	46.0
Subject	Mathematics Partial differential equations Statistical mechanics, structure of matter
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: UCLA
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-03-16
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0376994
URI	http://hdl.handle.net/2429/68807
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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