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Let $Z_n$ be an $(n\\times n)$-matrix chosen uniformly at random from the matrix analogue to the classical $\\ell_ p^n$-ball, defined as the set of all self-adjoint $(n\\times n)$-matrices satisfying $\\sum_{k=1}^n |\\lambda_k(A)|^p\\leq 1$. We prove a large deviations principle for the (random) spectral measure of the matrix $n^{1/p} Z_n$. As a consequence, we obtain that the spectral measure of $n^{1/p} Z_n$ converges weakly almost surely to a non-random limiting measure given by the Ullman distribution,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.04862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-14T19:04:26Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"33ef920eedb0aea533971e2c4478b6025bfda13f0e0d30603822bc932c5d8773","abstract_canon_sha256":"f4df872e9c26565f4905964f9cd9ae77351cd35b20ece3a5d16a410f622ac869"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:02.362410Z","signature_b64":"lXKXZAvt/btmGmGtSdMHf82atyOBg5v9um6OXQ2zK+8qUdSk9SwTSpwI4vlP2ZrXEu03xEtw0YZabhWwtsJeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a0d94c9ef3a956ff13da655107bf2318e6ddb413017709505adf763805120b8","last_reissued_at":"2026-05-18T00:08:02.361850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:02.361850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sanov-type large deviations in Schatten classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Joscha Prochno, Zakhar Kabluchko","submitted_at":"2018-08-14T19:04:26Z","abstract_excerpt":"Denote by $\\lambda_1(A), \\ldots, \\lambda_n(A)$ the eigenvalues of an $(n\\times n)$-matrix $A$. 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