TITLE: Divergence of Groups and Metric Spaces
QUESTION [9 upvotes]: Several papers, including this and this claim that divergence of finitely generated groups and metric spaces have been introduced by Misha Gromov in his paper "Asymptotic invariants of infinite groups". What is the precise reference and how did Gromov call this invariant?

REPLY [4 votes]: Here is (what I believe is) the relevant paragraph of the second "this", of which I am one of the co-authors. This paragraph contains a reference to a particular passage from Gromov's Asymptotic Invariants paper including a citation to the particular paragraph in that paper where the relevant discussion occurs.
In symmetric spaces of non-compact type, the order of the divergence of
geodesic rays is either exponential (when the rank is one) or linear (when the
rank is at least two). This inspired an initial thought that in the presence
of non-positive curvature the divergence must be either linear or exponential.
See [Gro93] for a discussion—an explicit statement of this conjecture appears
in 6.B2, subsection “Geometry of ∂T and Morse landscape at infinity,” Example
(h). In particular, Gromov stated an expectation that all pairs of geodesic
rays in the universal cover of a closed Riemannian manifold of non-positive
curvature diverge either linearly or exponentially [Gro93].