On mean outer radii of random polytopes
| Autor: | Alonso-Gutierrez, David, Dafnis, Nikos, Cifre, Maria A. Hernandez, Prochno, Joscha |
|---|---|
| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we introduce a new sequence of quantities for random polytopes. Let $K_N=\conv\{X_1,...,X_N\}$ be a random polytope generated by independent random vectors uniformly distributed in an isotropic convex body $K$ of $\R^n$. We prove that the so-called $k$-th mean outer radius $\widetilde R_k(K_N)$ has order $\max\{\sqrt{k},\sqrt{\log N}\}L_K$ with high probability if $n^2\leq N\leq e^{\sqrt{n}}$. We also show that this is also the right order of the expected value of $\widetilde R_k(K_N)$ in the full range $n\leq N\leq e^{\sqrt{n}}$. Comment: 14 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|