  In this work, we demonstrate that a functional modeling the self-aggregation
of stochastically distributed lipid molecules can be obtained as the
$\Gamma$-limit of a family of discrete energies driven by a sequence of
independent and identically distributed random variables. These random
variables are intended to describe the asymptotic behavior of lipid molecules
that satisfy an incompressibility condition. The discrete energy keeps into
account the interactions between particles. We resort to transportation maps to
compare functionals defined on discrete and continuous domains, and we prove
that, under suitable conditions on the scaling of these maps as the number of
random variables increases, the limit functional features an interfacial term
with a Wasserstein-type penalization.
