Timeline for (Novel?) notion of concentration/dispersion
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 24, 2019 at 5:51 | history | edited | Yuval Peres | CC BY-SA 4.0 |
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| Jul 24, 2019 at 4:20 | history | edited | Yuval Peres | CC BY-SA 4.0 |
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| Jul 23, 2019 at 18:53 | comment | added | Aryeh Kontorovich | Yuval, what if I take the $\inf$ over convex sets only? (Restricing to $\mathbb{R}^n$.) I think that would be a more useful definition -- have you seen it anywhere? | |
| Jul 23, 2019 at 18:52 | comment | added | Aryeh Kontorovich | I also realize that my definition is not as useful as I originally thought. Again, take $\nu$ to be the Lebesgue measure over $\mathbb{R}^n$ and let $\mu$ to be the mixture of very highly peaked Gaussians over a very large, widely spaced, finite grid. According to my notion, $\mu$ would be highly concentrated -- but for many interesting applications, we would actually say that $\mu$ is quite dispersed. | |
| Jul 23, 2019 at 18:49 | comment | added | Aryeh Kontorovich | Thanks, Yuval. I recognized the similarity to concentration functions, of course, but I recall seeing it defined differently -- $L(r)$ is the the sup of the complement of the measure of the $r$-blow-up over all sets of measure at least $1/2$. In other words, the notion that I'm familiar with uses a metric rather than a reference measure $\nu$. | |
| Jul 23, 2019 at 18:46 | vote | accept | Aryeh Kontorovich | ||
| Jul 23, 2019 at 17:27 | history | answered | Yuval Peres | CC BY-SA 4.0 |