  The neutron transport equation (NTE) describes the flux of neutrons across a
planar cross-section in an inhomogeneous fissile medium when the process of
nuclear fission is active. Classical work on the NTE emerges from the applied
mathematics literature in the 1950s through the work of R. Dautray and
collaborators, [7, 8, 19]. The NTE also has a probabilistic representation
through the semigroup of the underlying physical process when envisaged as a
stochastic process; cf. [7, 17, 18, 20]. More recently, [6] and [16] have
continued the probabilistic analysis of the NTE, introducing more recent ideas
from the theory of spatial branching processes and quasi-stationary
distributions. In this paper, we continue in the same vein and look at a
fundamental description of stochastic growth in the supercritical regime. Our
main result provides a significant improvement on the last known contribution
to growth properties of the physical process in [20], bringing neutron
transport theory in line with modern branching process theory such as [14, 12].
