{"id":"https://openalex.org/W7212540852","doi":"https://doi.org/10.48550/arxiv.2609.12940","title":"Large fluctuations of extended Rademacher random multiplicative functions","display_name":"Large fluctuations of extended Rademacher random multiplicative functions","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212540852","doi":"https://doi.org/10.48550/arxiv.2609.12940"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12940","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12940","pdf_url":"https://arxiv.org/pdf/2609.12940","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/2609.12940","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114619949","display_name":"Haozhe Gou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gou, Haozhe","raw_affiliation_strings":["Yau Mathematical Sciences Center , Tsinghua University , Beijing , 100084 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yau Mathematical Sciences Center , Tsinghua University , Beijing , 100084 , China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044509754","display_name":"Max Wenqiang Xu","orcid":"https://orcid.org/0000-0002-4964-0186","observed_orcids":["https://orcid.org/0000-0002-4964-0186"]},"institutions":[{"id":"https://openalex.org/I4403928416","display_name":"Beijing Institute of Mathematical Sciences and Applications","ror":"https://ror.org/05t6hvr95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4403928416","https://openalex.org/I99065089"]},{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Xu, Max Wenqiang","raw_affiliation_strings":["Beijing Institute of Mathematical Sciences and Applications , Beijing , 101408 , China","D\u00e9partement de math\u00e9matiques et de statistique , Universit\u00e9 de Montr\u00e9al , C. P. 6128 , succ. Centre-ville , Montr\u00e9al , QC H3C 3J7 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Mathematical Sciences and Applications , Beijing , 101408 , China","institution_ids":["https://openalex.org/I4403928416"]},{"raw_affiliation_string":"D\u00e9partement de math\u00e9matiques et de statistique , Universit\u00e9 de Montr\u00e9al , C. P. 6128 , succ. Centre-ville , Montr\u00e9al , QC H3C 3J7 , Canada","institution_ids":["https://openalex.org/I70931966"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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/T11329","display_name":"Limits and Structures in Graph Theory","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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/large-fluctuations","display_name":"large fluctuations","score":0.746999979019165},{"id":"https://openalex.org/keywords/random-multiplicative-functions","display_name":"random multiplicative functions","score":0.7710000276565552}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.830299973487854},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.821399986743927},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.7896999716758728},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5393999814987183},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.49799999594688416},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49549999833106995},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43529999256134033},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.35670000314712524},{"id":"https://openalex.org/C13929819","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Random function","level":3,"score":0.336899995803833},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12940","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12940","pdf_url":"https://arxiv.org/pdf/2609.12940","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.2609.12940","doi":"https://doi.org/10.48550/arxiv.2609.12940","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12940","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12940","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12940","pdf_url":"https://arxiv.org/pdf/2609.12940","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/W7212540852.pdf","grobid_xml":"https://content.openalex.org/works/W7212540852.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W2011729369","https://openalex.org/W2013285982","https://openalex.org/W2071523343","https://openalex.org/W2094924981","https://openalex.org/W2327183337","https://openalex.org/W2609926569","https://openalex.org/W2797990385","https://openalex.org/W3132753485","https://openalex.org/W3135907818","https://openalex.org/W3161659993","https://openalex.org/W4362598772","https://openalex.org/W4392489638","https://openalex.org/W4401827053","https://openalex.org/W4403184154","https://openalex.org/W4404985404","https://openalex.org/W4406733857","https://openalex.org/W7102752393","https://openalex.org/W7127269935","https://openalex.org/W7166706995","https://openalex.org/W7172274197","https://openalex.org/W7204116334"],"related_works":["https://openalex.org/W4405251462","https://openalex.org/W3135907818","https://openalex.org/W7172274197","https://openalex.org/W7127269935","https://openalex.org/W4403184154","https://openalex.org/W3161659993","https://openalex.org/W4362598772","https://openalex.org/W4406733857","https://openalex.org/W3132753485","https://openalex.org/W7204116334"],"abstract_inverted_index":{"Let":[0],"$f$":[1],"be":[2],"an":[3,49],"extended":[4],"Rademacher":[5],"random":[6],"multiplicative":[7],"function":[8,17],"(RMF).":[9],"We":[10],"show":[11],"that,":[12],"for":[13,29,84],"every":[14],"fixed":[15],"deterministic":[16],"$V(x)$":[18],"tending":[19],"to":[20,52,82],"infinity,":[21],"almost":[22,66],"surely":[23],"there":[24],"are":[25],"arbitrarily":[26],"large":[27,87],"$x$":[28,83],"which":[30],"\\[":[31],"\\sum_{n\\leq":[32],"x}f(n)":[33],"\\geq":[34],"\\frac{\\sqrt{x}(\\log\\log":[35],"x)^{1/4}}{V(x)}.":[36],"\\]":[37],"The":[38],"corresponding":[39],"negative":[40],"fluctuation":[41],"holds":[42],"as":[43],"well.":[44],"In":[45],"particular,":[46],"this":[47],"gives":[48],"affirmative":[50],"answer":[51],"Erd\u0151s":[53],"Problem~\\#1144.":[54],"As":[55],"a":[56,61],"byproduct,":[57],"our":[58],"result":[59],"has":[60],"direct":[62],"corollary":[63],"giving":[64],"new":[65],"sure":[67],"lower":[68],"bounds":[69],"$\\log\\log":[70],"x$":[71],"on":[72],"the":[73],"number":[74],"of":[75,78],"sign":[76],"changes":[77],"partial":[79],"sums":[80],"up":[81],"all":[85],"sufficiently":[86],"$x$.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}
