{"id":"https://openalex.org/W7214926667","doi":"https://doi.org/10.48550/arxiv.2609.37912","title":"Low discrepancy and spectral gap for directed hypergraphs via spectral regularity lemma for tensors","display_name":"Low discrepancy and spectral gap for directed hypergraphs via spectral regularity lemma for tensors","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214926667","doi":"https://doi.org/10.48550/arxiv.2609.37912"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37912","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37912","pdf_url":"https://arxiv.org/pdf/2609.37912","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017103214","display_name":"Hi\u1ec7p H\u00e0n","orcid":"https://orcid.org/0000-0001-7757-7244","observed_orcids":["https://orcid.org/0000-0001-7757-7244"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Han, Hiep","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017103214"],"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9990000128746033,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9990000128746033,"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/T11166","display_name":"Analytic Number Theory Research","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10849","display_name":"Finite Group Theory Research","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/directed-hypergraphs","display_name":"directed hypergraphs","score":0.8709999918937683},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.9990000128746033},{"id":"https://openalex.org/keywords/tensors","display_name":"tensors","score":0.859000027179718},{"id":"https://openalex.org/keywords/rank-one-decomposition","display_name":"rank-one decomposition","score":0.6650000214576721},{"id":"https://openalex.org/keywords/finite-abelian-groups","display_name":"finite abelian groups","score":0.9850000143051147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8195000290870667},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7953000068664551},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7067999839782715},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.663100004196167},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6166999936103821},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5300999879837036},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4966000020503998},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4941999912261963},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.414900004863739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3986999988555908},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.3977000117301941},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.3463999927043915},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37912","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37912","pdf_url":"https://arxiv.org/pdf/2609.37912","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.2609.37912","doi":"https://doi.org/10.48550/arxiv.2609.37912","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37912","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:2609.37912","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37912","pdf_url":"https://arxiv.org/pdf/2609.37912","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214926667.pdf","grobid_xml":"https://content.openalex.org/works/W7214926667.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7167849242","https://openalex.org/W2961783706","https://openalex.org/W2105457218","https://openalex.org/W7098973266","https://openalex.org/W3197284834","https://openalex.org/W3161557373","https://openalex.org/W3197127090","https://openalex.org/W7171541805","https://openalex.org/W2767120853","https://openalex.org/W4295571831"],"abstract_inverted_index":{"We":[0,91],"show":[1],"that":[2],"low":[3],"discrepancy":[4],"is":[5,36],"equivalent":[6],"to":[7],"spectral":[8,40],"gap":[9],"for":[10,43,85],"directed":[11],"$k$-uniform":[12],"hypergraphs.":[13],"For":[14],"undirected":[15],"hypergraphs":[16,44,103],"this":[17],"recovers":[18],"a":[19,26,37,60,67,95],"theorem":[20],"of":[21,33,50,63,78,101],"Lenz":[22],"and":[23,81,98],"Mubayi,":[24],"with":[25,70],"considerably":[27],"shorter":[28],"proof.":[29],"At":[30],"the":[31,47,99],"heart":[32],"our":[34],"argument":[35],"Frieze--Kannan":[38],"type":[39],"regularity":[41],"lemma":[42,75],"based":[45],"on":[46],"variational":[48],"notion":[49],"hypergraph":[51],"eigenvalues":[52],"by":[53],"Friedman--Wigderson,":[54],"which":[55],"decomposes":[56],"any":[57],"tensor":[58,69],"into":[59],"bounded":[61],"number":[62],"rank-one":[64],"tensors":[65],"plus":[66],"quasi-random":[68],"small":[71],"top":[72],"eigenvalue.":[73],"This":[74],"may":[76],"be":[77],"independent":[79],"interest,":[80],"we":[82],"prove":[83],"it":[84],"complex-valued,":[86],"not":[87],"necessarily":[88],"symmetric":[89],"tensors.":[90],"also":[92],"briefly":[93],"discuss":[94],"Szemer\u00e9di-type":[96],"variant":[97],"regularization":[100],"Cayley-type":[102],"over":[104],"finite":[105],"abelian":[106],"groups.":[107]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-01T00:00:00"}
