Timeline for Important (but not too well known) inequalities
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2020 at 8:37 | comment | added | Sam OT | @usul That is one of which I was not aware! It complements nicely the Berry--Esseen inequality | |
| Jun 21, 2020 at 8:35 | comment | added | Sam OT | @TerryTao I see, thank you for your insight :) | |
| Jun 21, 2020 at 4:31 | comment | added | usul | The DKW inequality on deviation of an empirical CDF from the ground truth is a very nice one. | |
| Jun 21, 2020 at 1:12 | comment | added | Terry Tao | Some individual inequalities in this class (e.g., the Chernoff inequality) may be fairly well known, but my sense is that the broader concentration of measure phenomenon (in particular, its applicability to nonlinear (but still Lipschitz or convex) functions of independent variables) is not widely known outside of the fields of mathematics that rely heavily on probability. | |
| Jun 20, 2020 at 15:09 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jun 20, 2020 at 14:44 | comment | added | Sam OT | [...cont] Various people who desire these bounded difference inequalities may not be aware of such 'typical' bounded difference inequalities where the bounds do not hold for all points in the space, but only for 'typical' ones, in some precise manner | |
| Jun 20, 2020 at 14:43 | comment | added | Sam OT | If I may add a suggestion to McDiarmid's inequality, which can be found in his survey On the Method of Bounded Differences, various authors have considered 'typical' bounded differences (as opposed to worst-case). See, for example, On the Method of Typical Bounded Differences [cont...] | |
| Jun 20, 2020 at 14:27 | comment | added | Sam OT | These are certainly very important inequalities! Would you describe them all as "unfamiliar to the majority of mathematicians"? Anyone who has done a masters level probability or theoretical statistics course is going to know the Chernoff and Azuma inequalities -- even an undergraduate course I attended did Chernoff and McDiarmid (aka bounded differences). Maybe as a young probabilist myself I am not in a good place to judge how well-known these are, though! | |
| Jun 20, 2020 at 3:41 | history | edited | Timothy Chow | CC BY-SA 4.0 |
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| Jun 20, 2020 at 2:21 | history | edited | Terry Tao | CC BY-SA 4.0 |
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| Jun 20, 2020 at 2:13 | history | answered | Terry Tao | CC BY-SA 4.0 |