  We show that a stochastic approach enables calculations of the optical
properties of large 2-dimensional and nanotubular excitonic molecular
aggregates. Previous studies of such systems relied on numerically
diagonalizing the dense and disordered Frenkel Hamiltonian, which scales
approximately as $\mathcal{O}(N^3)$ for $N$ dye molecules. Our approach scales
much more efficiently as $\mathcal{O}(N\log(N))$, enabling quick study of
systems with a million of coupled molecules on the micron size scale. We
calculate several important experimental observable including the optical
absorption spectrum and density of states, and develop a stochastic formalism
for the participation ratio. Quantitative agreement with traditional matrix
diagonalization methods is demonstrated for both small- and intermediate-size
systems. The stochastic methodology enables the study of the effects of
spatial-correlation in site energies on the optical signatures of large 2D
aggregates. Our results demonstrate that stochastic methods present a path
forward for screening structural parameters and validating experiments and
theoretical predictions in large excitonic aggregates.
