  In this article, we demonstrate that in a transport model of particles with
kinetic constraints, long-lived spatial structures are responsible for the
blocking dynamics and the decrease of the current at strong driving field.
Coexistence between mobile and blocked regions can be anticipated by a
first-order transition in the large deviation function for the current. By a
study of the system under confinement, we are able to study finite-size effects
and extract a typical length between mobile regions.
