  In this paper, we show the spectral convergence result of
$\overline{\partial}$-Laplacians when $(X,\omega)$ is a compact toric
symplectic manifold equipped with the natural prequantum line bundle $L$. We
consider a family $\{ J_s\}_s$ of $\omega$-compatible complex structures
tending to the large complex structure limit, and obtain the spectral
convergence of $\overline{\partial}$-Laplacians acting on $L^k$.
