  This paper presents a multiple length-scale asymptotic analysis for transport
problems in 1-D diffusive random media. This analysis shows that the
Levermore-Pomraning (LP) equations can be adjusted in order to achieve the
correct asymptotic behavior. This adjustment appears in the form of a rescaling
of the Markov transition functions by a factor $\eta$, which can be chosen in a
simple way. Numerical results are given that (i) validate the theoretical
predictions; and (ii) show that the adjusted LP equations greatly outperform
the standard LP model for this class of transport problems.
