Measurements of consecutive sites in a many body qudit system (e.q. a spin chain) can be interpreted as generating a probabilistic sequence of numbers $X_1 X_2 X_3 \ldots$, where $X_i\in \{0,1,\ldots,d-1 \}$.
Are there any studies on that approach, in particular - exploring predictability of such systems or constructing a Markov model of some order simulating it?