  We give two constructions of Gaussian-like random holomorphic sections of a
Hermitian holomorphic line bundle $(L,h_{L})$ on a Hermitian complex manifold
$(X,\Theta)$. In particular, we are interested in the case where the space of
$\mathcal{L}^2$-holomorphic sections $H^{0}_{(2)}(X,L)$ is infinite
dimensional. We first provide a general construction of Gaussian random
holomorphic sections of $L$, which, if $\dim H^{0}_{(2)}(X,L)=\infty$, are
almost never $\mathcal{L}^2$-integrable on $X$. The second construction
combines the abstract Wiener space theory with the Berezin-Toeplitz
quantization and yields a random $\mathcal{L}^2$-holomorphic section.
Furthermore, we study their random zeros in the context of semiclassical
limits, including their equidistribution, large deviation estimates and hole
probabilities.
