Timeline for Less regular version of the Gaussian free field
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2020 at 16:30 | comment | added | Abdelmalek Abdesselam | I didn't use a reference. It's easy to figure out by hand. | |
| Jan 18, 2020 at 12:47 | comment | added | truebaran | @AbdelmalekAbdesselam thank you for your comment-could you please give me some reference for this statement regarding white noise? | |
| Jan 17, 2020 at 19:47 | comment | added | Abdelmalek Abdesselam | Also, the case of $L^2$ with the $\psi$'s given by Hermite functions leads to white noise rather than the GFF. | |
| Jan 17, 2020 at 19:45 | comment | added | Abdelmalek Abdesselam | To have some receptacle which is a bit more canonical, one can also take $W=\mathcal{S}'(\mathbb{R}^d)$ for $\Omega=\mathbb{R}^d$. | |
| Jan 17, 2020 at 19:29 | comment | added | Nate Eldredge | In general, a sum of the form $\sum \xi_k \psi_k$, where $\psi_k$ is an orthonormal set in a Hilbert space $H$, will diverge almost surely in the topology of $H$. It is always possible to find some larger space $W$ with a weaker topology (possibly again Hilbert or Banach), with a dense embedding of $H$ into $W$, such that the sum converges i.p. in $W$. The resulting "object" depends entirely on the choice of $W$, though. | |
| Jan 17, 2020 at 16:52 | history | asked | truebaran | CC BY-SA 4.0 |