Title	On a question of Assaf Naor
Creator	Oleszkiewicz, Krzysztof
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2017-06-01T15:00
Description	For any separable Banach space $(F,\\| \cdot \\|)$ and independent $F$-valued random vectors $X$ and $Y$ such that ${\mathbf E} \\|X\\|, {\mathbf E} \\|Y\\|< \infty$, we have \[ \inf_{z \in F} ({\mathbf E}\\|X-z\\|+{\mathbf E}\\|Y-z\\|) \leq 3 \cdot {\mathbf E}\\| X-Y\\|. \] Indeed, it suffices to consider $z=({\mathbf E} X+{\mathbf E} Y)/2$ and use Jensen's inequality. Assaf Naor asked whether the constant $3$ in the inequality is optimal. We will discuss this and related problems.
Extent	45 minutes
Subject	Mathematics; Probability theory and stochastic processes; Statistics; Probability / statistical mechanics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Warsaw
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2017-11-29
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0360766
URI	http://hdl.handle.net/2429/63755
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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