Timeline for Two mixing rates of random dynamical system

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Apr 14, 2019 at 16:52	comment	added	Anthony Quas		At the level of intuition, yes. At the level of proof, no. You could, no doubt, build counter examples to that statement. But they would be artificial, but if you had a concrete system of that type in front of you, you should expect the behaviour you’re talking about. You would still have to work hard to prove it.
Apr 14, 2019 at 13:25	comment	added	jason		@Anthony Quas Thanks for the example. But with the same setting of your example, assume decay rate of all $T_1$ is $e^{-n}$ , decay rate of all $T_0$ is $e^{-\sqrt{n}}$. Then the decay rate of any mix of $T_0$ and $T_1$ should be lying between them, and less than $e^{-\sqrt{n}}$. Can I deduce the decay rate of any mix of $T_0$ and $T_1$ is less than $e^{-\sqrt{n}}$ without $C_{\omega}$?
Apr 13, 2019 at 19:34	comment	added	Anthony Quas		The $C_\omega$ is completely natural. You should imagine that you are applying two dynamical systems:$T_0$ and $T_1$ (so $\omega$ is a sequence of 0’s and 1’s). Imagine $T_1$ mixes much faster than $T_0$. Now if $\omega$ has a large number of initial 0’s, the mixing will be slow, so $C_\omega$ should be large. You would expect $C$ not to depend on $\onega$ if all of the fiber maps mix at the same rate.
S Apr 13, 2019 at 16:16	history	suggested	user64494	CC BY-SA 4.0	A typo in the title is corrected.
Apr 13, 2019 at 14:57	review	Suggested edits
S Apr 13, 2019 at 16:16
Apr 12, 2019 at 21:29	history	asked	jason	CC BY-SA 4.0