{"id":"https://openalex.org/W7225659209","doi":"https://doi.org/10.13140/rg.2.2.25097.81761","title":"Absolutely Continuous Laws on a Bounded Interval Are Completely Mixable for All Large n","display_name":"Absolutely Continuous Laws on a Bounded Interval Are Completely Mixable for All Large n","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225659209","doi":"https://doi.org/10.13140/rg.2.2.25097.81761"},"language":"en","primary_location":{"id":"doi:10.13140/rg.2.2.25097.81761","doi":"https://doi.org/10.13140/rg.2.2.25097.81761","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.25097.81761","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24070252","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041315596","display_name":"Yitzchak Shmalo","orcid":"https://orcid.org/0000-0002-2886-3049","observed_orcids":["https://orcid.org/0000-0002-2886-3049"]},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yitzchak Shmalo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041315596"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T11720","display_name":"Probability and Risk Models","score":0.8223000168800354,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.8223000168800354,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.11819999665021896,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.009100000374019146,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/absolutely-continuous-distributions","display_name":"absolutely continuous distributions","score":0.765999972820282},{"id":"https://openalex.org/keywords/bounded-interval","display_name":"bounded interval","score":0.6660000085830688},{"id":"https://openalex.org/keywords/sums-of-random-variables","display_name":"sums of random variables","score":0.5350000262260437},{"id":"https://openalex.org/keywords/uniform-distribution","display_name":"uniform distribution","score":0.5249999761581421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8292999863624573},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7757999897003174},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.6596999764442444},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6402000188827515},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.4578000009059906},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36660000681877136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3617999851703644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3544999957084656},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.31040000915527344},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.13140/rg.2.2.25097.81761","doi":"https://doi.org/10.13140/rg.2.2.25097.81761","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.25097.81761","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24070252","doi":"https://doi.org/10.5281/zenodo.24070252","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24070252","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24070253","doi":"https://doi.org/10.5281/zenodo.24070253","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24070253","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24070252","doi":"https://doi.org/10.5281/zenodo.24070252","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24070252","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7213941466","https://openalex.org/W2605465523","https://openalex.org/W1493971734","https://openalex.org/W2360575220","https://openalex.org/W2892636537","https://openalex.org/W2357517837","https://openalex.org/W2380246823","https://openalex.org/W2380358776","https://openalex.org/W2378275570","https://openalex.org/W2114661861"],"abstract_inverted_index":{"A":[0],"distribution":[1],"$F$":[2],"is":[3,18,34,42,57,88,98,121,151],"$n$-completely":[4,43,58,89,122],"mixable":[5,59,90,123],"if":[6],"there":[7],"are":[8],"$n$":[9],"random":[10],"variables,":[11],"each":[12],"with":[13,82,198],"law":[14,29,52,77,101,114,132,187],"$F$,":[15],"whose":[16,32],"sum":[17,150,190],"almost":[19],"surely":[20],"constant.":[21],"Puccetti,":[22],"Wang":[23,25,46],"and":[24,45,71,157],"proved":[26],"that":[27,75,108,148,168],"a":[28,54,79,83,100,144,196,199],"on":[30,38,53,78,102,115,143],"$[a,b]$":[31,41],"density":[33],"at":[35],"least":[36],"$3/(n(b-a))$":[37],"all":[39,61,92],"of":[40,105,118,130,154,164,188,191],"mixable,":[44],"asked":[47],"whether":[48],"every":[49,76,125],"absolutely":[50,85],"continuous":[51,86,200],"bounded":[55,80],"interval":[56,81,104,117],"for":[60,91,124],"sufficiently":[62],"large":[63,93],"$n$.":[64,94],"We":[65],"answer":[66],"this":[67],"in":[68,183],"the":[69,112,128,131,137,140,159,165,172,181,186,189],"affirmative,":[70],"more":[72],"generally":[73],"show":[74],"nonzero":[84,201],"part":[87],"The":[95,175],"main":[96],"step":[97],"quantitative:":[99],"an":[103,116],"length":[106,119],"$R$":[107,153],"dominates":[109,195],"$q$":[110],"times":[111],"uniform":[113,141,166,173],"$2H$":[120],"$n\\ge(6R/H+1)/q$,":[126],"whatever":[127],"rest":[129],"is.":[133],"Its":[134],"proof":[135],"couples":[136],"copies":[138,167,182,194],"outside":[139],"component":[142],"quantile":[145],"grid,":[146],"so":[147],"their":[149],"within":[152],"its":[155],"mean,":[156],"absorbs":[158],"error":[160],"by":[161,179],"linear":[162],"tilts":[163],"average":[169],"out":[170],"to":[171],"law.":[174],"general":[176],"case":[177],"follows":[178],"grouping":[180],"pairs,":[184],"since":[185],"two":[192],"independent":[193],"measure":[197],"density.":[202]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
