{"id":"https://openalex.org/W7220976264","doi":"https://doi.org/10.48550/arxiv.2610.09725","title":"Tameness of transitive Boolean functions","display_name":"Tameness of transitive Boolean functions","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220976264","doi":"https://doi.org/10.48550/arxiv.2610.09725"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09725","pdf_url":"https://arxiv.org/pdf/2610.09725","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/2610.09725","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123434512","display_name":"Xinyu Long","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Long, Xinyu","raw_affiliation_strings":["School of Mathematics Shandong University , Jinan , Shandong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics Shandong University , Jinan , Shandong , China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5123434512"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9409000277519226,"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":0.9409000277519226,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.010499999858438969,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.00570000009611249,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-functions","display_name":"Boolean functions","score":0.8619999885559082},{"id":"https://openalex.org/keywords/transitivity","display_name":"transitivity","score":0.7829999923706055},{"id":"https://openalex.org/keywords/tightness","display_name":"tightness","score":0.6510000228881836},{"id":"https://openalex.org/keywords/fourier-projection","display_name":"Fourier projection","score":0.7860000133514404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7906000018119812},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6636000275611877},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.5965999960899353},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5952000021934509},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5943999886512756},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5924999713897705},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.5554999709129333},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5306000113487244},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4788999855518341},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4681999981403351},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.34119999408721924},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2840000092983246},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09725","pdf_url":"https://arxiv.org/pdf/2610.09725","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.2610.09725","doi":"https://doi.org/10.48550/arxiv.2610.09725","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09725","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:2610.09725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09725","pdf_url":"https://arxiv.org/pdf/2610.09725","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":[{"id":"https://openalex.org/G7955825103","display_name":null,"funder_award_id":"ZR2024JQ030","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220976264.pdf","grobid_xml":"https://content.openalex.org/works/W7220976264.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3034328592","https://openalex.org/W3108780116","https://openalex.org/W2949574901","https://openalex.org/W184836871","https://openalex.org/W2972764304","https://openalex.org/W7100420957","https://openalex.org/W2065321712","https://openalex.org/W4376639505","https://openalex.org/W3138532527","https://openalex.org/W6988950980"],"abstract_inverted_index":{"Let":[0],"$f_n:\\{0,1\\}^n\\to\\{0,1\\}$":[1],"be":[2],"Boolean":[3],"functions,":[4],"and":[5,40,60],"let":[6],"$C_n$":[7],"count":[8],"their":[9],"changes":[10],"in":[11,19,55],"a":[12,70,83],"unit":[13],"time":[14],"interval":[15],"under":[16],"stationary":[17],"dynamics":[18],"which":[20],"each":[21],"coordinate":[22],"is":[23,38,77],"independently":[24],"resampled":[25],"at":[26],"rate":[27],"one":[28],"from":[29],"the":[30,56,80],"Bernoulli$(p_n)$":[31],"distribution.":[32],"We":[33],"prove":[34],"that,":[35],"if":[36],"$f_n$":[37],"transitive":[39],"$n\\min\\{p_n,1-p_n\\}^{r}\\to\\infty$":[41],"for":[42],"every":[43],"$r>0$,":[44],"then":[45],"tightness":[46],"of":[47,82],"$(C_n)$":[48],"implies":[49],"$\\mathrm{Var}(f_n)\\to0$.":[50],"This":[51],"settles":[52],"Forsstr\u00f6m's":[53],"conjecture":[54],"$p_n\\le":[57],"1/2$":[58],"regime":[59],"extends":[61],"it":[62],"symmetrically":[63],"to":[64],"arbitrary":[65],"biases.":[66],"The":[67],"proof":[68],"uses":[69],"mixed":[71],"jump":[72],"sum":[73],"whose":[74],"second":[75],"moment":[76],"bounded":[78],"by":[79],"generator":[81],"low":[84],"degree":[85],"Fourier":[86],"projection.":[87]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-09T00:00:00"}