Timeline for Change of variables in a Gaussian integral in matrix form
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 2, 2022 at 2:58 | history | edited | Michael Hardy | CC BY-SA 4.0 | edited body |
| Jan 17, 2021 at 1:52 | comment | added | Iosif Pinelis | @Rafael : I am not good at providing references. You may want to look at Theorem 4 of Terence Tao's notes at terrytao.wordpress.com/2008/02/04/254a-lecture-9-ergodicity/… , as well as at the references given in Wikipedia article. | |
| Jan 16, 2021 at 22:41 | vote | accept | Rafael | ||
| Jan 16, 2021 at 22:41 | vote | accept | Rafael | ||
| Jan 16, 2021 at 22:41 | |||||
| Jan 15, 2021 at 20:05 | comment | added | Rafael | @losifPInelis do you know of any good references to learn more about the desintegration of a measure? | |
| Jan 15, 2021 at 2:37 | comment | added | Rafael | @CarloBeenakker, how do you define the delta function measure? This seems like what I'm looking for, but I'm unsure of how to justify my decision of measure. | |
| Jan 15, 2021 at 1:35 | comment | added | Iosif Pinelis | @CarloBeenakker : Unfortunately, I don't understand how this delta function measure on the plane is defined. | |
| Jan 14, 2021 at 21:40 | comment | added | Carlo Beenakker | if I may, the integral defined in the first line of my answer defines a delta function measure on the plane $x=\sum_j y_j$; there should be no ambiguity in that calculation. | |
| Jan 14, 2021 at 20:35 | history | edited | Iosif Pinelis | CC BY-SA 4.0 | added 23 characters in body |
| Jan 14, 2021 at 19:13 | comment | added | Iosif Pinelis | @Rafael : I have added a remark that should help one understand how the measures $\mu_t$ are constructed. | |
| Jan 14, 2021 at 19:11 | history | edited | Iosif Pinelis | CC BY-SA 4.0 | added 994 characters in body |
| Jan 14, 2021 at 18:50 | history | edited | Iosif Pinelis | CC BY-SA 4.0 | added 421 characters in body |
| Jan 14, 2021 at 18:35 | comment | added | Iosif Pinelis | @Rafael : As I said, I do not see any measures on the plane defined in the other answers. Also, I do not see good ways to introduce measures in those answers. | |
| Jan 14, 2021 at 18:26 | comment | added | Rafael | I'm not sure I understand. What would be, for example, the measure from the below example and my first method and how does it differ from the Lebesgue measure? What is then the measure from the second method? And thank you very much for the comment, your answers always help a lot. | |
| Jan 14, 2021 at 17:56 | comment | added | Iosif Pinelis | @Rafael : As I said, the other answers are different because they deal with integrals over undefined measures. Therefore, those integrals were undefined, and thus you cannot possibly attach any value to them. | |
| Jan 14, 2021 at 17:18 | comment | added | Rafael | I'm confused now, because this also differs from the answer form @CarloBeenakker. I indeed want to integrate over a measure induced by the Lebesgue measure, but do you know why all the answers are different? The presence or absence of the factor $\frac{1}{\sqrt{k}}$ is importante for me. | |
| Jan 14, 2021 at 17:03 | history | edited | Iosif Pinelis | CC BY-SA 4.0 | added 253 characters in body |
| Jan 14, 2021 at 16:52 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |