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We prove that the eigenfunctions of $H$ are typically supported in a set of approximately $NT$ sites, thereby confirming the existence of a previously conjectured non-ergodic delocalized phase. Our proof is based on martingale estimates along the characteristic curves of the stochastic advection equation satisfied by the local resolvent of the Brownian motion representation of $H$."},"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":"1709.10313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-29T10:09:16Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP","math.PR"],"title_canon_sha256":"52c98fdb723caf103e28942a78a46470426186699809ced85b20b18e3ccaa447","abstract_canon_sha256":"e0031d8d342b9f287d8016c7ff5eb462fe370616f895f47539cf27ee7b677455"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:34.421044Z","signature_b64":"IjBQ4um4lQmU9bh7kW3yWxhd5wR59wSbIOM2ym7yzNPmlCZU/eDjEo+5mm99AEOvBaj+abMVbdfu1uViH/WCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fd4caefee7729bbfb366f43e3f34bd789674992416e799d3b1c1d0b68f9e1a1","last_reissued_at":"2026-05-17T23:51:34.420389Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:34.420389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Ergodic Delocalization in the Rosenzweig-Porter Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Per von Soosten, Simone Warzel","submitted_at":"2017-09-29T10:09:16Z","abstract_excerpt":"We consider the Rosenzweig-Porter model $H = V + \\sqrt{T}\\, \\Phi$, where $V$ is a $N \\times N$ diagonal matrix, $\\Phi$ is drawn from the $N \\times N$ Gaussian Orthogonal Ensemble, and $N^{-1} \\ll T \\ll 1$. We prove that the eigenfunctions of $H$ are typically supported in a set of approximately $NT$ sites, thereby confirming the existence of a previously conjectured non-ergodic delocalized phase. 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