Timeline for Connections between two constructions of infinite dimensional Gaussian measures
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 31, 2020 at 17:08 | comment | added | JustWannaKnow | I see. I think this confusion of mine is worth a new post, to put it some context. Anyway, you've been really helpful! Thanks a lot! | |
| May 31, 2020 at 17:03 | comment | added | user69642 | I understand your question this way: what is the difference between white noise distribution theory and Malliavin calculus ? In the first theory, the white noise (derivative of Brownian motion) is the central object of interest whereas in the second it is Brownian motion. Both theories have several similarities but they are intrinsically different by nature. | |
| May 31, 2020 at 15:05 | comment | added | JustWannaKnow | I'm still having trouble understanding the origin of such differences. My main interest is statistical mechanics. I've been reading the section Gaussian Free Field (GFF) of two different books and the Hamiltonian on both books is the same. But when the time comes to discuss the thermodynamic limit, one book goes in the $l^{2}(\mathbb{Z}^{d})$ direction and the other goes in the $s'$ direction. But it seems that the target here is the same, but the constructions are differente and the results are different. Do you know why? | |
| May 31, 2020 at 14:29 | comment | added | user69642 | The underlying probability space is $s'$ then $\langle ;f\rangle$ is the random variable $X$ defined, for all $\omega \in s'$, by $$X(\omega) = \langle \omega; f \rangle$$. The ``difficulty" is that the bilinear pairing is defined for $\omega \in s'$ if $f$ belongs to $s$ and only $\mu_C$ a.e.if $f$ belongs to $\ell^2(\mathbb{Z}^d)$. | |
| May 31, 2020 at 11:52 | history | answered | user69642 | CC BY-SA 4.0 |