{"paper":{"title":"Local Spectrum of Truncations of Kronecker Products of Haar Distributed Unitary Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Brendan Farrell, Raj Rao Nadakuditi","submitted_at":"2013-11-26T19:31:12Z","abstract_excerpt":"We address the local spectral behavior of the random matrix $\\Pi_1 U^{\\otimes k} \\Pi_2 U^{\\otimes k *} \\Pi_1$, where $U$ is a Haar distributed unitary matrix of size $n\\times n$, the factor $k$ is at most $c_0\\log n$ for a small constant $c_0>0$, and $\\Pi_1,\\Pi_2$ are arbitrary projections on $\\ell_2^{n^k}$ of ranks proportional to $n^k$. We prove that in this setting the $k$-fold Kronecker product behaves similarly to the well-studied case when $k=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6783","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"}