Timeline for Why does non-decreasing entropy imply actual convergence to that max entropy distribution?
Current License: CC BY-SA 4.0
10 events
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| Nov 28, 2022 at 7:10 | comment | added | Arrow | @usul I was under the impression the entropic line of reasoning uses monotonicity, your (3), and some argument about the "gap", and combines them to prove convergence to a Gaussian. I'm asking about the "gap" argument. | |
| Nov 27, 2022 at 21:28 | comment | added | usul | Hm. So your question is about the fact (1) Xn converges to something that maximizes entropy, but you want a fundamentally different answer than the pair of facts (2) Xn converges to a Gaussian and (3) Gaussians maximize entropy. Seems hard to disentangle. | |
| Nov 27, 2022 at 17:27 | comment | added | Arrow | @MichaelHardy better? | |
| Nov 27, 2022 at 17:26 | history | edited | Arrow | CC BY-SA 4.0 |
added 268 characters in body
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| Nov 27, 2022 at 5:49 | answer | added | Iosif Pinelis | timeline score: 2 | |
| Nov 27, 2022 at 2:30 | comment | added | Michael Hardy | The normal distribution maximizes the entropy subject to constraints that specify the expectation and the variance. That any such constraints are considered is completely camouflaged by your way of stating the "famous result". Can you rephrase it to be clear about that? | |
| S Nov 27, 2022 at 1:29 | history | suggested | J. W. Tanner | CC BY-SA 4.0 |
Corrected English
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| Nov 27, 2022 at 1:10 | review | Suggested edits | |||
| S Nov 27, 2022 at 1:29 | |||||
| Nov 27, 2022 at 0:39 | comment | added | Iosif Pinelis | Do you have a reference to the monotonicity? Also, how is the (differential entropy?) $\mathrm H$ defined (say for non-absolutely continuous distributions)? | |
| Nov 26, 2022 at 13:44 | history | asked | Arrow | CC BY-SA 4.0 |