Timeline for If the pointwise ergodic theorem holds along all subsequences with nonzero natural density, is the system strong mixing?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2023 at 10:32 | vote | accept | Nate River | ||
| Sep 15, 2023 at 3:52 | history | became hot network question | |||
| Sep 15, 2023 at 1:44 | answer | added | Terry Tao | timeline score: 16 | |
| Sep 14, 2023 at 23:20 | comment | added | Terry Tao | ... unfortunately, the best known mixing rates for this shift (see arxiv.org/abs/2308.00823 ) are a little bit too slow to get the pointwise convergence from a van der Corput / Borel-Cantelli argument. But if one can find a non-strongly mixing system which has a mixing rate faster than a large power of $1/\log N$ (rather than a small power) then I think one is in business. | |
| Sep 14, 2023 at 20:28 | comment | added | Terry Tao | The Chacon subshift in the answer to mathoverflow.net/questions/47080/… looks like a good candidate for a counterexample (though verifying the pointwise ergodic theorem may require a certain amount of combinatorial analysis). | |
| Sep 14, 2023 at 19:50 | history | asked | Nate River | CC BY-SA 4.0 |