A common construction in statistics is the distribution of $n$ iid random variables, for $n$ arbitrarily large. For large enough $n$ the distribution is approximately uniform over a highly regular typical set in $n$-space.
The "letter-typicality" definition essentially resembles a quotient of a large permutation group, or more properly the disjoint union of relatively few highly similar quotients.
Information theory often studies covering, packing and projection of these sets. These spatial intuitions are not studied directly in any presentation I have seen. Does anyone know of any articles or books that make this connection precise? It would be especially useful to see an approach that clarifies the essential structure across many trials of two or more jointly-distributed random variables.