  A crinkled subordinator is an $\ell^2$-valued random process which can be
thought of as a version of the usual one-dimensional subordinator with each out
of countably many jumps being in a direction orthogonal to the directions of
all other jumps. We show that the path of a $d$-dimensional random walk with
$n$ independent identically distributed steps with heavy-tailed distribution of
the radial components and asymptotically orthogonal angular components
converges in distribution in the Hausdorff distance up to isometry and also in
the Gromov--Hausdorff sense, if viewed as a random metric space, to the closed
range of a crinkled subordinator, as $d,n\to\infty$.
