{"paper":{"title":"Operator $\\ell_p\\to\\ell_q$ norms of Gaussian matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Marta Strzelecka, Rafa{\\l} Lata{\\l}a","submitted_at":"2025-02-04T10:01:59Z","abstract_excerpt":"We confirm the conjecture posed by Gu\\'edon, Hinrichs, Litvak, and Prochno in 2017 that $\\mathbb{E}\\|(a_{ij}g_{ij})_{i\\le m, j\\le n}\\colon \\ell_p^n \\to \\ell_q^m\\|$ is comparable, up to constants depending only on $p$ and $q$, to \\[ \\max_i \\|(a_{ij})_j\\|_{p^*} +\\max_j \\|(a_{ij})_i\\|_{q} +\\mathbb{E} \\max_{i,j} |a_{ij}g_{ij}| \\] provided that $1\\le p \\le 2\\le q \\le \\infty$. This was known before only in the case $p=1$ or $q=\\infty$, and in the spectral case $p=2=q$. We also reprove the conjecture in the case $p=2=q$ without using spectral theory (which was employed in the previously known proof)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02186","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.02186/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}