Timeline for Is this Markov chain of Gaussian matrix products $G_1 G_2 \dots G_m$ ergodic?
Current License: CC BY-SA 4.0
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| Jan 5, 2023 at 13:02 | comment | added | kvphxga | @JosephVanName what kind of normalization will make the chain ergodic? so if product of singular values of $G_i$s is $1$ it becomes ergodic? | |
| Jan 5, 2023 at 11:59 | vote | accept | kvphxga | ||
| Jan 5, 2023 at 1:28 | answer | added | R W | timeline score: 2 | |
| Jan 5, 2023 at 1:24 | comment | added | Joseph Van Name | I do not think they are ergodic since a standard computer experiment shows that as $t\rightarrow\infty$, $X_t$ gets closer and closer to becoming rank-1 matrix. I do not think it is too hard to show that the rank-1 matrices are an attractor. Did you also want to make the determinant of each $G_i$ have absolute value 1 or at least normalize the norm? | |
| Jan 5, 2023 at 0:30 | comment | added | kvphxga | meant the Gaussian matrices, referring to this kind of coupling. Thought it's pretty standard terminology, does it need to further details? mmss.wcas.northwestern.edu/thesis/articles/get/1052/… | |
| Jan 5, 2023 at 0:29 | history | edited | kvphxga | CC BY-SA 4.0 |
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| S Jan 5, 2023 at 0:22 | history | suggested | Buzz | CC BY-SA 4.0 |
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| Jan 5, 2023 at 0:13 | comment | added | Buzz | What do you mean by "coupling"? Because your condition on $\operatorname{Pr}(X_t\neq Y_t)$ doesn't seem to make sense; that probability seems like it is unavoidably going to be 1. | |
| Jan 5, 2023 at 0:12 | review | Suggested edits | |||
| S Jan 5, 2023 at 0:22 | |||||
| Jan 4, 2023 at 23:50 | history | edited | kvphxga | CC BY-SA 4.0 |
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| Jan 4, 2023 at 23:45 | history | edited | kvphxga | CC BY-SA 4.0 |
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| Jan 4, 2023 at 23:38 | history | asked | kvphxga | CC BY-SA 4.0 |