{"id":"https://openalex.org/W7212049537","doi":"https://doi.org/10.48550/arxiv.2609.06237","title":"Probability-theoretic interpretation of degeneracy locus formulas","display_name":"Probability-theoretic interpretation of degeneracy locus formulas","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W7212049537","doi":"https://doi.org/10.48550/arxiv.2609.06237"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06237","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06237","pdf_url":"https://arxiv.org/pdf/2609.06237","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.06237","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012296700","display_name":"Rich\u00e1rd Rim\u00e1nyi","orcid":"https://orcid.org/0000-0002-7978-7883","observed_orcids":["https://orcid.org/0000-0002-7978-7883"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rimanyi, Richard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5012296700"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/degeneracy-loci","display_name":"degeneracy loci","score":0.9039999842643738},{"id":"https://openalex.org/keywords/symmetric-maps","display_name":"symmetric maps","score":0.7379999756813049},{"id":"https://openalex.org/keywords/chebyshev-moments","display_name":"Chebyshev moments","score":0.9739999771118164},{"id":"https://openalex.org/keywords/enumerative-geometry","display_name":"enumerative geometry","score":0.5130000114440918},{"id":"https://openalex.org/keywords/interpretation-of-probability","display_name":"probability interpretation","score":0.335999995470047}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8037999868392944},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.5748999714851379},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5472999811172485},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5315999984741211},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36419999599456787},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.34929999709129333},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31619998812675476},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.29170000553131104}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06237","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06237","pdf_url":"https://arxiv.org/pdf/2609.06237","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.06237","doi":"https://doi.org/10.48550/arxiv.2609.06237","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06237","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.06237","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06237","pdf_url":"https://arxiv.org/pdf/2609.06237","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212049537.pdf","grobid_xml":"https://content.openalex.org/works/W7212049537.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1857155239","https://openalex.org/W2969231171","https://openalex.org/W3093486351","https://openalex.org/W3129014886"],"related_works":["https://openalex.org/W1565192513","https://openalex.org/W2803983690","https://openalex.org/W2791382371","https://openalex.org/W4390915860","https://openalex.org/W2341915509","https://openalex.org/W7105612463","https://openalex.org/W1983598924","https://openalex.org/W2027189291","https://openalex.org/W2287742759","https://openalex.org/W2983821436"],"abstract_inverted_index":{"Schwartz-MacPherson":[0],"classes":[1,50,59],"of":[2,5,37,42,53,63],"degeneracy":[3],"loci":[4],"symmetric":[6,58],"and":[7,56],"skew-symmetric":[8],"maps.":[9],"Together":[10],"with":[11],"the":[12,21,26,38,48,57,64],"known":[13],"formulas":[14,33],"for":[15,25],"ordinary":[16],"linear":[17],"maps,":[18],"this":[19],"completes":[20],"stable":[22],"SSM":[23],"theory":[24],"three":[27],"classical":[28],"types.":[29],"We":[30],"interpret":[31],"these":[32],"probabilistically,":[34],"in":[35],"terms":[36],"endpoint":[39],"random":[40,65],"partition":[41],"a":[43],"stochastic":[44],"rational":[45],"six-vertex":[46],"model:":[47],"skew":[49],"are":[51,60],"probabilities":[52],"Maya-dimer":[54],"events,":[55],"Chebyshev":[61],"moments":[62],"2-core.":[66]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
