On the geometry of random polytopes

2019/02/05 by Shahar Mendelson, Mendelson, Shahar · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities #Random Matrices and Applications

paper · doi:10.48550/arxiv.1902.01664

openalex publication_date 2019/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a simple proof to a fact recently established in [5]: let ξ be a symmetric random variable that has variance 1, let Γ=(ξ_ij) be an N × n random matrix whose entries are independent copies of ξ, and set X₁,...,X_N to be the rows of Γ. Then under minimal assumptions on ξ and as long as N ≥ c₁n, c₂ (B_∞ⁿ ∩ √(log(eN/n)) B₂ⁿ ) ⊂ \rm absconv(X₁,...,X_N) with high probability.

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