{"public_id":"co_9d4dea67b6d9cd864f7809435ef7e90b","status":"active","merged_into_public_id":null,"resolved_public_id":"co_9d4dea67b6d9cd864f7809435ef7e90b","name":"Gaussian β ensemble","description":"A random matrix ensemble with a general β parameter, studied here for its eigenvalue density and resolvent expansions.","aliases":[],"types":["model"],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"concept","status":"active","confidence":null,"origin_kinds":["extraction","extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":1,"verifier_classes":["system"],"verifier_class_counts":{"system":1,"user_agent":0},"verdict_counts":{"approve":1,"reject":0},"verifier_state":"system_only","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","concept.status"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"papers":[{"corpus_id":32962314,"title":"Moments of the Gaussian $\\beta$ Ensembles and the large-$N$ expansion of the densities","citation_count":56,"url":"https://sah.borca.ai/papers/32962314"}],"claims":[{"public_id":"cl_5bf071a86002cd7bb772f89b1114cec4","text":"The loop equation formalism is used to compute the 1/N expansion of the resolvent for the Gaussian β ensemble up to and including the term at O(N^{-6}).","corpus_id":32962314,"url":"https://sah.borca.ai/claims/cl_5bf071a86002cd7bb772f89b1114cec4"},{"public_id":"cl_8cf261a74c08d97d9a32c9f1e6d8dac8","text":"The moments of the eigenvalue density are computed up to and including the 12-th power.","corpus_id":32962314,"url":"https://sah.borca.ai/claims/cl_8cf261a74c08d97d9a32c9f1e6d8dac8"},{"public_id":"cl_d4d81649097b5cf2017e7f78c67d6a8a","text":"The smoothed density is expanded up to and including the term at O(N^{-6}), containing non-integrable singularities at the endpoints of the support.","corpus_id":32962314,"url":"https://sah.borca.ai/claims/cl_d4d81649097b5cf2017e7f78c67d6a8a"}],"related_concepts":[],"resolved_url":"https://sah.borca.ai/concepts/co_9d4dea67b6d9cd864f7809435ef7e90b","url":"https://sah.borca.ai/concepts/co_9d4dea67b6d9cd864f7809435ef7e90b"}