  In this paper, we investigate extreme singular values of the analysis matrix
of a Gabor frame $(g, \Lambda)$ with a random window $g$. Columns of such
matrices are time and frequency shifts of $g$, and $\Lambda\subset
\mathbb{Z}_M\times\mathbb{Z}_M$ is the set of time-frequency shift indices. Our
aim is to obtain bounds on the singular values of such random time-frequency
structured matrices for various choices of the frame set $\Lambda$, and to
investigate their dependence on the structure of $\Lambda$, as well as on its
cardinality. We also compare the results obtained for Gabor frame analysis
matrices with the respective results for matrices with independent identically
distributed entries.
