The 2009 course on GFA by Roman Vershynin (https://www.math.uci.edu/~rvershyn/papers/GFA-book.pdf) introduced the subject with this line on the course page, "Geometric functional analysis studies high dimensional linear structures. Some examples of such structures are Euclidean and Banach spaces, convex sets and linear operators in high dimensions. A central question of geometric functional analysis is: what do typical n-dimensional structures look like when n grows to infinity?"

Now in recent times there have been high-dimensional information theory courses like this, http://www.stat.yale.edu/~yw562/teaching/598/index.html and Vershynin has himself written a (very famous!) book on high-dimensional probability http://www-personal.umich.edu/~romanv/papers/HDP-book/HDP-book.pdf

• Is it possible to see the contents of the above new courses and books as new and modern forms of GFA? Are there any specific famous results which embody such a relationship?

I do feel that there is a strong overlap among these 3 but I would like to know if there is a well-established technically precise view of the relationship between them.