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A partial Laplacian as an infinitesimal generator on the Wasserstein space Gangbo, Wilfrid Apr 10, 2018
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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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https://iiif.library.ubc.ca/presentation/dsp.48630.1-0376994/manifest