{"paper":{"title":"On the Maximum of Random Variables on Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Joscha Prochno, Stiene Riemer","submitted_at":"2012-03-16T19:08:59Z","abstract_excerpt":"Let $\\xi_i$, $i=1,...,n$, and $\\eta_j$, $j=1,...,m$ be iid p-stable respectively q-stable random variables, $1<p<q<2$. We prove estimates for $\\Ex_{\\Omega_1} \\Ex_{\\Omega_2}\\max_{i,j}\\abs{a_{ij}\\xi_i(\\omega_1)\\eta_j(\\omega_2)}$ in terms of the $\\ell_p^m(\\ell_q^n)$-norm of $(a_{ij})_{i,j}$. Additionally, for p-stable and standard gaussian random variables we prove estimates in terms of the $\\ell_p^m(\\ell_{M_{\\xi}}^n)$-norm, $M_{\\xi}$ depending on the Gaussians. Furthermore, we show that a sequence $\\xi_i$, $i=1,...,n$ of iid $\\log-\\gamma(1,p)$ distributed random variables ($p\\geq 2$) generates a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3788","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}