Timeline for Concentration of infinite-dimensional Gaussian measure
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jul 21, 2016 at 13:32 | comment | added | Fedor Goncharov | From the notes of Natan Eldredge again I found a beautiful fact that one can find the support of Gaussian measure via the following way: $$supp \mu=\bigcap\limits_{q(f)=0}Ker(f),$$ where $q$ -- is the quadratic form on the dual space: $$q(f)=\int_X f^2(x)\mu(dx).$$ This formula is nice, but gives support of measure in terms of topology of $X$. But for the case when $X=R^{\infty}$ and $\mu =\prod_{k=1}^{\infty} \mathcal{N}_{\lambda_k}$, where $\lambda_k >0$ is a variance, $supp \mu=R^\infty$, which does not relfect concentration on $\ell_2$ for small $\lambda_k$ | |
| Jul 3, 2016 at 7:27 | review | First posts | |||
| Jul 3, 2016 at 9:43 | |||||
| Jul 3, 2016 at 7:24 | history | asked | Fedor Goncharov | CC BY-SA 3.0 |