2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136014We prove a quantitative version of the bound on the smallest singular value of a Bernoulli covariance matrix (due to Bai and Yin). Then we use this bound, together with several recent developments, to show that the distance from a random (1-delta) n - dimensional section of ell_1^n, realised as an image of a sign matrix, to an Euclidean ball is polynomial in 1/delta (and independent of n), with high probability.22 pagesFunctional AnalysisMathematical PhysicsMetric Geometrytext