  In this theoretical study, we explore F\"orster resonant energy transfer of a
single exciton within a two-dimensional array of self-assembled quantum dots
arranged randomly on a circular mesa. Employing the stochastic simulation
method, we solve the equation of motion for the density matrix, considering a
specified decay rate. Our analysis quantifies diffusion through the mean-square
displacement from the initially excited quantum dot, revealing distinct
temporal stages: ballistic, normal diffusion, and saturation. Furthermore, we
observe power-law localization of the exciton. Complementing our numerical
investigations, we develop approximate analytical expressions that closely
align with the numerical findings.
