text: In this paper, we investigate extreme singular values of the analysis matrix of a Gabor frame @math with a random window @math . Columns of such matrices are time and frequency shifts of @math , and @math 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 @math , and to investigate their dependence on the structure of @math , 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.
  @cite_1: We prove an optimal estimate of the smallest singular value of a random sub- Gaussian matrix, valid for all dimensions. For an Nn matrix A with inde- pendent and identically distributed sub-Gaussian entries, the smallest singular value of A is at least of the order p Np n � 1 with high probability. A sharp
summary: The following optimal estimate of the smallest singular value of the analysis matrix for a random subgaussian frame with independent entries is due to Rudelson and Vershynin @cite_1 .