{"id":"https://openalex.org/W7212186385","doi":"https://doi.org/10.48550/arxiv.2609.10530","title":"Fluctuations of additive martingale limits of branching Brownian motion","display_name":"Fluctuations of additive martingale limits of branching Brownian motion","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212186385","doi":"https://doi.org/10.48550/arxiv.2609.10530"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.10530","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10530","pdf_url":"https://arxiv.org/pdf/2609.10530","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/2609.10530","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100354363","display_name":"Xinxin Chen","orcid":"https://orcid.org/0000-0001-8064-7020","observed_orcids":["https://orcid.org/0000-0001-8064-7020","https://orcid.org/0000-0001-6521-5983"]},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Xinxin","raw_affiliation_strings":["Beijing Normal University , School of Mathematical Sciences , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Normal University , School of Mathematical Sciences , China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087115883","display_name":"Michel Pain","orcid":"https://orcid.org/0000-0003-1849-1429","observed_orcids":["https://orcid.org/0000-0003-1849-1429"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4405258862","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210092408","https://openalex.org/I4210126056","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pain, Michel","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulouse , Universit\u00e9 de Toulouse , CNRS , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse , Universit\u00e9 de Toulouse , CNRS , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4405258862","https://openalex.org/I84500057"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"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":0.9994999766349792,"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/T11720","display_name":"Probability and Risk Models","score":9.999999747378752e-05,"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/T10067","display_name":"Stochastic processes and financial applications","score":9.999999747378752e-05,"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/branching-brownian-motion","display_name":"branching Brownian motion","score":0.9990000128746033},{"id":"https://openalex.org/keywords/critical-branching-processes","display_name":"critical branching processes","score":0.6320000290870667},{"id":"https://openalex.org/keywords/subcritical-regime","display_name":"subcritical regime","score":0.7459999918937683},{"id":"https://openalex.org/keywords/fluctuations","display_name":"fluctuations","score":0.6240000128746033},{"id":"https://openalex.org/keywords/almost-sure-convergence","display_name":"almost sure convergence","score":0.968999981880188}],"concepts":[{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.8266000151634216},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7739999890327454},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6499999761581421},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.5216000080108643},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4848000109195709},{"id":"https://openalex.org/C162344956","wikidata":"https://www.wikidata.org/wiki/Q6777133","display_name":"Martingale representation theorem","level":5,"score":0.47870001196861267},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.4512999951839447},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4097999930381775},{"id":"https://openalex.org/C30268764","wikidata":"https://www.wikidata.org/wiki/Q3707378","display_name":"Martingale difference sequence","level":3,"score":0.3946000039577484},{"id":"https://openalex.org/C2779806530","wikidata":"https://www.wikidata.org/wiki/Q4956437","display_name":"Branching random walk","level":3,"score":0.3855000138282776},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3149000108242035},{"id":"https://openalex.org/C53920899","wikidata":"https://www.wikidata.org/wiki/Q4976524","display_name":"Brownian excursion","level":5,"score":0.29660001397132874},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.29350000619888306},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2680000066757202},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C185637853","wikidata":"https://www.wikidata.org/wiki/Q1242402","display_name":"Doob's martingale inequality","level":4,"score":0.2648000121116638},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.10530","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10530","pdf_url":"https://arxiv.org/pdf/2609.10530","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":"pmh:oai:HAL:hal-05745098v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05745098v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.10530","doi":"https://doi.org/10.48550/arxiv.2609.10530","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.10530","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:2609.10530","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10530","pdf_url":"https://arxiv.org/pdf/2609.10530","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":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212186385.pdf","grobid_xml":"https://content.openalex.org/works/W7212186385.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W3137662970","https://openalex.org/W4390136854","https://openalex.org/W4401202637","https://openalex.org/W4414460025","https://openalex.org/W4417172810","https://openalex.org/W4417523322","https://openalex.org/W7125911226"],"related_works":["https://openalex.org/W3137662970","https://openalex.org/W2807710905","https://openalex.org/W4410798416","https://openalex.org/W4401202637","https://openalex.org/W2963034579","https://openalex.org/W4392752829","https://openalex.org/W2758653759","https://openalex.org/W3199184376","https://openalex.org/W2016134839","https://openalex.org/W1505812758"],"abstract_inverted_index":{"Consider":[0],"a":[1,98,127],"one-dimensional":[2],"branching":[3],"Brownian":[4],"motion.":[5],"Let":[6],"$W_\\infty(\u03b2)$":[7],"denote":[8],"the":[9,12,16,26,29,44,72,117,124],"limit":[10,27],"of":[11,28,54,119],"additive":[13,121],"martingale":[14,31],"in":[15,75],"subcritical":[17],"regime":[18],"$\\lvert":[19],"\u03b2\\rvert":[20],"<":[21],"\u03b2_c$":[22],"and":[23,105,123],"$Z_\\infty$":[24],"be":[25],"derivative":[30],"at":[32],"criticality.":[33],"Madaule":[34],"(Stochastic":[35],"Process.":[36],"Appl.":[37],"126":[38],"(2016),":[39],"no.":[40],"2,":[41],"470--502)":[42],"established":[43],"following":[45],"convergence":[46,77],"\\[":[47,80],"\\frac{W_\\infty(\u03b2)}{\u03b2_c-\u03b2}\\xrightarrow[\u03b2\\nearrow":[48],"\u03b2_c]{\\mathbb{P}}":[49],"2Z_\\infty.":[50],"\\]":[51,91],"The":[52],"goal":[53],"this":[55,62,76],"paper":[56],"is":[57],"twofold:":[58],"firstly,":[59],"we":[60,70],"strengthen":[61],"result":[63],"into":[64],"an":[65],"almost":[66],"sure":[67],"convergence;":[68],"secondly,":[69],"describe":[71],"fluctuations":[73,125],"occurring":[74],"by":[78],"proving":[79],"\\frac{1}{\u03b2_c-\u03b2}\\left(":[81],"\\frac{W_\\infty(\u03b2)}{\u03b2_c-\u03b2}":[82],"-":[83],"2":[84],"Z_\\infty":[85],"+2(\u03b2_c-\u03b2)\\log(\u03b2_c-\u03b2)":[86],"Z_\\infty\\right)":[87],"\\xrightarrow[\u03b2\\nearrow":[88],"\u03b2_c]{(d)}":[89],"S,":[90],"where,":[92],"conditionally":[93],"on":[94],"$Z_\\infty$,":[95],"$S$":[96],"follows":[97],"spectrally":[99],"negative":[100],"1-stable":[101],"distribution":[102],"with":[103],"scale":[104],"shift":[106],"parameters":[107],"proportional":[108],"to":[109,116,126],"$Z_\\infty$.":[110],"Furthermore,":[111],"these":[112],"results":[113],"are":[114],"extended":[115],"setting":[118],"complex":[120],"martingales":[122],"multi-dimensional":[128],"convergence.":[129]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-11T00:00:00"}
