{"id":"https://openalex.org/W7213499490","doi":"https://doi.org/10.48550/arxiv.2609.18835","title":"Degree-Free Spectral Independence for Log-Concave Holant Measures","display_name":"Degree-Free Spectral Independence for Log-Concave Holant Measures","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213499490","doi":"https://doi.org/10.48550/arxiv.2609.18835"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18835","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18835","pdf_url":"https://arxiv.org/pdf/2609.18835","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/2609.18835","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132890802","display_name":"Xiaoyu Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chen, Xiaoyu","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151993321","display_name":"Zejia Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Zejia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5152021879","display_name":"Xinyuan Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhang, Xinyuan","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.2142000049352646,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.2142000049352646,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.2134000062942505,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.13770000636577606,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spectral-independence","display_name":"spectral independence","score":0.9610000252723694},{"id":"https://openalex.org/keywords/glauber-dynamics","display_name":"Glauber dynamics","score":0.8980000019073486},{"id":"https://openalex.org/keywords/relaxation-time","display_name":"relaxation time","score":0.8700000047683716},{"id":"https://openalex.org/keywords/monomer-dimer-model","display_name":"monomer-dimer model","score":0.996999979019165},{"id":"https://openalex.org/keywords/b-matching","display_name":"b-matching","score":0.9110000133514404},{"id":"https://openalex.org/keywords/simple-graphs","display_name":"simple graphs","score":0.6930000185966492},{"id":"https://openalex.org/keywords/markov-chain-mixing","display_name":"Markov chain mixing","score":0.5920000076293945},{"id":"https://openalex.org/keywords/gpt-5-6","display_name":"GPT-5.6","score":0.6759999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7329999804496765},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6168000102043152},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5981000065803528},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5530999898910522},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42419999837875366},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C2780708879","wikidata":"https://www.wikidata.org/wiki/Q5567254","display_name":"Glauber","level":3,"score":0.336899995803833},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3361999988555908},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3314000070095062},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2915000021457672},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2840000092983246},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.25529998540878296}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18835","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18835","pdf_url":"https://arxiv.org/pdf/2609.18835","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.2609.18835","doi":"https://doi.org/10.48550/arxiv.2609.18835","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18835","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:2609.18835","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18835","pdf_url":"https://arxiv.org/pdf/2609.18835","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/W7213499490.pdf","grobid_xml":"https://content.openalex.org/works/W7213499490.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1514725634","https://openalex.org/W2755288388","https://openalex.org/W2898617375","https://openalex.org/W2996822558","https://openalex.org/W3127673302","https://openalex.org/W3172764972","https://openalex.org/W4226518768","https://openalex.org/W4307334779","https://openalex.org/W4307450986","https://openalex.org/W4316652322","https://openalex.org/W4367369689","https://openalex.org/W4385327666","https://openalex.org/W4387816403","https://openalex.org/W4399523733","https://openalex.org/W4411075545","https://openalex.org/W7128627869","https://openalex.org/W7155489944","https://openalex.org/W7204461376"],"related_works":["https://openalex.org/W4307334779","https://openalex.org/W3097115680","https://openalex.org/W4367369689","https://openalex.org/W4220905732","https://openalex.org/W2611336766","https://openalex.org/W7100972546","https://openalex.org/W4404407076","https://openalex.org/W3214333250","https://openalex.org/W3159235954","https://openalex.org/W3202753626"],"abstract_inverted_index":{"We":[0],"establish":[1],"a":[2,16],"degree-independent":[3],"bound":[4,53],"on":[5,12],"spectral":[6],"independence":[7],"for":[8,22,27,36],"log-concave":[9],"Holant":[10],"problems":[11],"simple":[13],"graphs.":[14],"As":[15],"corollary,":[17],"we":[18],"obtain":[19],"relaxation-time":[20,52],"bounds":[21],"Glauber":[23],"dynamics":[24],"of":[25,46],"$O_\u03bb(m)$":[26],"the":[28,44,51],"monomer-dimer":[29],"model":[30],"at":[31,38],"activity":[32],"$\u03bb$":[33],"and":[34],"$O_{b,\u03bb}(m)$":[35],"$b$-matchings":[37],"fugacity":[39],"$\u03bb>0$,":[40],"where":[41],"$m$":[42],"is":[43],"number":[45],"edges.":[47],"For":[48],"uniform":[49],"$b$-matchings,":[50],"improves":[54],"to":[55],"$O(bm)$.":[56],"The":[57],"main":[58],"proof":[59],"ideas":[60],"were":[61],"found":[62],"using":[63],"GPT-5.6":[64],"Sol.":[65]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}
