  We investigate theoretically the stochastic dynamics of Resonance Electronic
Energy Transfer (RET), in a bi-dimensional overexcited ensemble of donor and
acceptor molecules. We find that, after initial optical excitation of all the
donors, the reaction kinetics is well-described by a non-linear mean-field
theory. The latter provides a solid way to define and compute an effective rate
of RET, even for disordered samples. We predict that this effective rate scales
as $\left\langle R \right\rangle^{\alpha}$ with $\left\langle R \right\rangle$
the average distance between individual excited donors and their
nearest-neighbor acceptor molecules, and $\alpha \in \left\lbrack -6,-2
\right\rbrack$ an exponent depending on the spatial distribution of molecular
pairs in the sample. Using a kinetic Monte-Carlo approach, we show departures
from this macroscopic mean-field description arising from fluctuations and
spatial correlations between several molecules involved in the RET process. We
expect this prediction to be relevant for both molecular science and biology,
where the control and optimization of the RET dynamics is a key issue.
