I seem to have resolved, affirmatively, an open question I'd posed in Sec. 6.5.3 of my thesis -- namely, whether for (just about) any mixing matrix there's a measure achieving those mixing coefficients. I haven't written up a proof yet, but looks like it'll make a cute little result. Here's a very short writeup (no proof); let me know if you want to hear more.

Got an interesting conjecture regarding mixing coefficients of random fields. I can see this one having far-reaching implications but unfortunately see no proof...

[Update: that random field mixing conjecture is wrong. Maximal graph degree is too crude a measure of connectivity -- seems like some sort of path counting is necessary...]

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