  Reduced models are matrix integrals believed to be related to the large N
limit of gauge theories. These integrals are known to simplify further when the
number of matrices D (corresponding to the number of space-time dimensions in
the gauge theory) becomes large. Even though this limit appears to be of little
use for computing the standard rectangular Wilson loop (which always singles
out two directions out of D), a meaningful large D limit can be defined for a
randomized Wilson loop (in which all D directions contribute equally). In this
article, a proof-of-concept demonstration of this approach is given for the
simplest reduced model (the original Eguchi-Kawai model) and the simplest
randomization of the Wilson loop (Brownian sum over random walks). The
resulting averaged Wilson loop displays a scale behavior strongly reminiscent
of the area law.
