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In our work we present fully analytical description of the angular spectrum and correlations of bright squeezed vacuum and explain the anisotropy effects and the effect of spatial walk-off from the point of view of the Schmidt modes. We show that by only tilting of the crystal it is possible to obtain giant twin-beam generation that can be used in different applications. The obtained theoretical results are compared with the experimental data in high-gain regime and are found to be in a good agreement. The physics of the found effects is explained in terms of collective Schmidt modes of the system.