{"paper":{"title":"Free fermions and $\\alpha$-determinantal processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math.MP","math.PR","quant-ph"],"primary_cat":"math-ph","authors_text":"Fabio Deelan Cunden, Neil O'Connell, Satya N. Majumdar","submitted_at":"2018-11-28T13:47:52Z","abstract_excerpt":"The $\\alpha$-determinant is a one-parameter generalisation of the standard determinant, with $\\alpha=-1$ corresponding to the determinant, and $\\alpha=1$ corresponding to the permanent. In this paper a simple limit procedure to construct $\\alpha$-determinantal point processes out of fermionic processes is examined. The procedure is illustrated for a model of $N$ free fermions in a harmonic potential. When the system is in the ground state, the rescaled correlation functions converge for large $N$ to determinants (of the sine kernel in the bulk and the Airy kernel at the edges). We analyse the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11556","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":""},"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"}