Talk:Concentration of measure

Citation[edit]

It might be nice to add a link to the following book. I'll let someone who is better than me at linking to books do it. The book: The Concentration of Measure Phenomenon by Michel Ledoux, ISBN-10: 0821828649, ISBN-13: 978-0821828649 Lavaka 02:54, 7 January 2007 (UTC)[reply]

Done. Thanks. Oleg Alexandrov (talk) 23:34, 7 January 2007 (UTC)[reply]

Thank you Lavaka 18:51, 10 January 2007 (UTC)[reply]

suprenum not infimum or do i misunderstand smth.?[edit]

...where the ~~infimum~~ suprenum is over all 1-Lipschitz functions... —Preceding unsigned comment added by 217.232.18.115 (talk) 17:13, 18 May 2008 (UTC)[reply]

Need explanation[edit]

Can someone explain metric measure space or however it was worded, it took so long for me to figure out how to write here that I forgot what I was asking. — Preceding unsigned comment added by Punstress (talk • contribs) 19:50, 8 October 2012 (UTC)[reply]

$x_{0}$ not defined[edit]

The section "Concentration on the sphere" uses a variable $x_{0}$ that is never defined. --188.22.38.215 (talk) 07:42, 15 April 2017 (UTC)[reply]

"Lévy's Lemma"[edit]

The phrase "Lévy's Lemma" is often used for referring to the results discussed in this article^[1]^[2]^[3], especially in the context of quantum information; since there's no article of that name on Wikipedia, a redirection to this article would be appreciated.

^ Popescu, Sandu; et al. (17 Oct 2016). "The foundations of statistical mechanics from entanglement: Individual states vs. averages" (PDF). arXiv:0511225.
^ McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018). Barren plateaus in quantum neural network training landscapes. Nature Communications, 9(1), 4812. https://doi.org/10.1038/s41467-018-07090-4
^ Manuel Gerken, Measure concentration: Levy’s Lemma, 2013, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.679.2560&rep=rep1&type=pdf

Liouville measure[edit]

The link attached to "Liouville measure" in the section "Concentration of measure in physics" leads to an article on "Symplectic manifold". This seems like an accident, or at the very least, not helpful for people wanting to know about the Liouville measure. Clarification? Thanks!

Verbatim text from/in uncited source[edit]

I'm not sure if this should be included as a citation or is a plagiarism (used in the lightest possible sense) of the wikipedia text, but very similar language can be found in these notes:

https://web.math.princeton.edu/~naor/homepage%20files/Concentration%20of%20Measure.pdf Borholquib (talk) 16:28, 20 March 2024 (UTC)[reply]

[1] Popescu, Sandu; et al. (17 Oct 2016). "The foundations of statistical mechanics from entanglement: Individual states vs. averages" (PDF). arXiv:0511225.

[2] McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018). Barren plateaus in quantum neural network training landscapes. Nature Communications, 9(1), 4812. https://doi.org/10.1038/s41467-018-07090-4

[3] Manuel Gerken, Measure concentration: Levy’s Lemma, 2013, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.679.2560&rep=rep1&type=pdf

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