  We introduce a Gibbs measure on nearest-neighbour paths of length $t$ in the
Euclidean $d$-dimensional lattice, where each path is penalised by a factor
proportional to the size of its boundary and an inverse temperature $\beta$. We
prove that, for all $\beta>0$, the random walk condensates to a set of diameter
$(t/\beta)^{1/3}$ in dimension $d=2$, up to a multiplicative constant. In all
dimensions $d\ge 3$, we also prove that the volume is bounded above by
$(t/\beta)^{d/(d+1)}$ and the diameter is bounded below by
$(t/\beta)^{1/(d+1)}$. Similar results hold for a random walk conditioned to
have local time greater than $\beta$ everywhere in its range when $\beta$ is
larger than some explicit constant, which in dimension two is the logarithm of
the connective constant.
