  We study the asymptotic behavior of the principal eigenvalue of a weakly
coupled, cooperative linear elliptic system in a stationary ergodic
heterogeneous medium. The system arises as the so-called multigroup diffusion
model for neutron flux in nuclear reactor cores, the principal eigenvalue
determining the criticality of the reactor in a stationary state. Such systems
have been well-studied in recent years in the periodic setting, and the purpose
of this work is to obtain results in random media. Our approach connects the
linear eigenvalue problem to a system of quasilinear viscous Hamilton-Jacobi
equations. By homogenizing the latter, we characterize the asymptotic behavior
of the eigenvalue of the linear problem and exhibit some concentration behavior
of the eigenfunctions.
