Timeline for Does mixing automatically imply this seemingly stronger "uniform modulo re-ordering" version of mixing?
Current License: CC BY-SA 4.0
11 events
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| May 3, 2023 at 1:22 | comment | added | user65023 | @JulianNewman It is an interesting question!! Thank you for the positive feedback. I'm aware of the multiple mixing question. I didn't see how to get a proof, but have thought about constructing a counterexample. It would need to be infinite rank, and might as well be zero entropy, since if there is a counterexample, then there must be a zero entropy counterexample. | |
| May 3, 2023 at 0:59 | comment | added | Julian Newman | I've now written the proof as a new answer; my idea about transfer operators didn't work, but I've found an alternative way to adapt your answer to the question that I asked. Thank you again! | |
| May 2, 2023 at 19:50 | comment | added | Julian Newman | PS: I wonder if a similar kind of approach could be used to make progress towards the currently open problem of whether mixing implies 3-mixing. That is: Let $T$ be a mixing transformation of a probability space $(X,\mathcal{B},\mu)$; is it necessarily the case that for all $A,B,C \in \mathcal{B}$ and $\varepsilon>0$ there exists $N\in\mathbb{N}$ such that for all $n_1 \geq N$ and all $n_2 \geq N$, $|\mu(A \cap T^{-n_1}(B) \cap T^{-(n_1+n_2)}(C))-\mu(A)\mu(B)\mu(C)|<\varepsilon$? | |
| May 2, 2023 at 19:45 | comment | added | Julian Newman | Beautiful!! Thank you!! Actually, you've answered with the roles of $A$ and $B$ reversed from the actual question that I asked; but I'm pretty sure that, by replacing what is effectively the Koopman operator in your argument with the transfer operator, your argument goes through to get the result I want. I will try and write this up soon as a new answer. | |
| May 1, 2023 at 18:51 | comment | added | user65023 | No worries! Someday I expect to pose as an online chatbot for a side hustle. | |
| May 1, 2023 at 11:32 | history | edited | Stefan Kohl♦ | CC BY-SA 4.0 |
Added the link to the cited paper.
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| May 1, 2023 at 11:09 | history | edited | user65023 | CC BY-SA 4.0 |
added 108 characters in body
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| May 1, 2023 at 10:23 | comment | added | mathworker21 | Very nice!! I apologize for my comment on your other answer. You had a new account and at first the reference you gave just seemed completely unrelated! | |
| Apr 30, 2023 at 21:26 | review | Late answers | |||
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| S Apr 30, 2023 at 21:11 | review | First answers | |||
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| S Apr 30, 2023 at 21:11 | history | answered | user65023 | CC BY-SA 4.0 |