Timeline for Expectation of a function of two entries of an isotropic unit vector $\mathbb{E}_{\mathbf{w}\sim\mathcal{S}^{p-1}}\![{w_{1}}^{\!4}\,{w_{2}}^{\!4}]$
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7 events
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| Aug 17, 2023 at 6:41 | comment | added | Itay | Thank you. Using your references I became aware with Haar integrals. My question here can be solved as a special case of Eq. (24) in "Integrals of monomials over the orthogonal group" (Gorin 2002). That is, I am only interested in monomials of entries of random matrices from the Haar measure. | |
| Aug 14, 2023 at 14:30 | comment | added | Abdelmalek Abdesselam | @Itay: Sure. FYI, I linked to my other question on moments for Grassmannians because this relates to the generation of random orthogonal vectors, e.g., taking the first two columns of a Haar distributed orthogonal matrix. My question is for unitary matrices, but the same ideas also apply to orthogonal random matrices. | |
| Aug 13, 2023 at 9:52 | comment | added | Itay | Thank you professor! These are interesting techniques. I will read further about them. | |
| Aug 11, 2023 at 16:58 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Aug 11, 2023 at 16:36 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Aug 11, 2023 at 16:28 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
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| Aug 11, 2023 at 16:22 | history | answered | Abdelmalek Abdesselam | CC BY-SA 4.0 |