{"paper":{"title":"Top eigenpair statistics of diluted Wishart matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Barak Budnick, Fabio Caccioli, Pierpaolo Vivo, Preben Forer, Sabrina Aufiero, Silvia Bartolucci","submitted_at":"2025-01-31T16:43:28Z","abstract_excerpt":"Using the replica method, we compute the statistics of the top eigenpair of diluted covariance matrices of the form $\\mathbf{J} = \\mathbf{X}^T \\mathbf{X}$, where $\\mathbf{X}$ is a $N\\times M$ sparse data matrix, in the limit of large $N,M$ with fixed ratio and a bounded number of nonzero entries. We allow for random non-zero weights, provided they lead to an isolated largest eigenvalue. By formulating the problem as the optimisation of a quadratic Hamiltonian constrained to the $N$-sphere at low temperatures, we derive a set of recursive distributional equations for auxiliary probability densi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19280","kind":"arxiv","version":2},"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/2501.19280/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"}