{"id":"https://openalex.org/W7214004668","doi":"https://doi.org/10.48550/arxiv.2609.23069","title":"Feasible Frontiers for Sub-Gamma Envelopes: the Variance--Pole Trade-off for Infinitely Divisible Laws","display_name":"Feasible Frontiers for Sub-Gamma Envelopes: the Variance--Pole Trade-off for Infinitely Divisible Laws","publication_year":2026,"publication_date":"2026-09-19","ids":{"openalex":"https://openalex.org/W7214004668","doi":"https://doi.org/10.48550/arxiv.2609.23069"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23069","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23069","pdf_url":"https://arxiv.org/pdf/2609.23069","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/2609.23069","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5149607572","display_name":"Yichuan Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1328775524","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55","country_code":"CN","type":"education","lineage":["https://openalex.org/I1328775524"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Yichuan","raw_affiliation_strings":["School of Art and Design , Zhejiang Sci-Tech University , Hangzhou , 310018 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Art and Design , Zhejiang Sci-Tech University , Hangzhou , 310018 , China","institution_ids":["https://openalex.org/I1328775524"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152449595","display_name":"Xin Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1328775524","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55","country_code":"CN","type":"education","lineage":["https://openalex.org/I1328775524"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Xin","raw_affiliation_strings":["School of Art and Design , Zhejiang Sci-Tech University , Hangzhou , 310018 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Art and Design , Zhejiang Sci-Tech University , Hangzhou , 310018 , China","institution_ids":["https://openalex.org/I1328775524"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1328775524"],"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/T13500","display_name":"Probability and Statistical Research","score":0.7968999743461609,"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"}},"topics":[{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.7968999743461609,"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/T11720","display_name":"Probability and Risk Models","score":0.1476999968290329,"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":0.006599999964237213,"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/infinitely-divisible-distributions","display_name":"infinitely divisible distributions","score":0.9229999780654907},{"id":"https://openalex.org/keywords/cumulant-generating-function","display_name":"cumulant generating function","score":0.7649999856948853},{"id":"https://openalex.org/keywords/third-cumulant","display_name":"third cumulant","score":0.6639999747276306},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"exponential distribution","score":0.42399999499320984},{"id":"https://openalex.org/keywords/variational-formula","display_name":"variational formula","score":0.4480000138282776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8341000080108643},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5346999764442444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4542999863624573},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4318999946117401},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.413100004196167},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.39480000734329224},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3176000118255615},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.3077999949455261},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2743000090122223},{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.25929999351501465}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23069","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23069","pdf_url":"https://arxiv.org/pdf/2609.23069","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.2609.23069","doi":"https://doi.org/10.48550/arxiv.2609.23069","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23069","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:2609.23069","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23069","pdf_url":"https://arxiv.org/pdf/2609.23069","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214004668.pdf","grobid_xml":"https://content.openalex.org/works/W7214004668.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4414981929","https://openalex.org/W7207662383","https://openalex.org/W7207751277"],"related_works":["https://openalex.org/W7207662383","https://openalex.org/W7207751277","https://openalex.org/W7216156739","https://openalex.org/W7095158172","https://openalex.org/W2091193732","https://openalex.org/W7207592338","https://openalex.org/W7223342720","https://openalex.org/W2610858089","https://openalex.org/W2395578269","https://openalex.org/W2071541632"],"abstract_inverted_index":{"A":[0,66],"right":[1],"sub-gamma":[2],"bound":[3],"is":[4,18,38,90,97,154,206],"described":[5],"by":[6],"a":[7,12,39,42,79,109,115,124,163,172,197,214,225,235,238],"quadratic":[8,35],"proxy":[9],"$v$":[10,26],"and":[11,15,82,93,166],"pole":[13,119,137],"$c$,":[14],"the":[16,28,32,55,59,62,71,88,104,128,143,152,160,168,186,190,204,209,221],"pair":[17,202],"not":[19,41],"unique:":[20],"enlarging":[21],"either":[22,180],"preserves":[23],"it.":[24],"Fixing":[25],"at":[27,34,133,178,196,213,241],"variance":[29,52],"$V$":[30,179],"removes":[31],"ambiguity":[33],"order":[36],"but":[37],"convention,":[40],"consequence.":[43],"For":[44],"centered":[45,236],"infinitely":[46],"divisible":[47],"laws":[48],"with":[49,158,175],"finite":[50],"nonzero":[51],"we":[53],"determine":[54],"entire":[56],"boundary":[57,170],"of":[58,101,103],"feasible":[60,95],"set,":[61],"map":[63],"$v\\mapsto":[64],"c_*(v)$.":[65],"Beta$(1,2)$":[67],"multiplier":[68],"applied":[69],"to":[70,208,231],"normalised":[72],"Kolmogorov":[73],"canonical":[74],"measure":[75],"turns":[76],"feasibility":[77],"into":[78],"one-dimensional":[80],"comparison":[81],"yields":[83],"an":[84],"exact":[85,191],"variational":[86],"formula:":[87],"frontier":[89,144,188,205],"convex,":[91],"nonincreasing,":[92],"its":[94],"set":[96],"convex.":[98],"The":[99],"abscissa":[100],"convergence":[102],"moment":[105],"generating":[106,211],"function":[107,212],"imposes":[108],"$v$-insensitive":[110],"floor":[111],"on":[112,121,203],"$c_*$,":[113],"so":[114],"law":[116],"whose":[117],"variance-exact":[118],"sits":[120],"it":[122],"has":[123,162],"flat":[125],"frontier,":[126],"whereas":[127],"third-cumulant":[129],"obstruction":[130],"exists":[131],"only":[132],"$v=V$.":[134],"Whenever":[135],"that":[136,218],"lies":[138],"strictly":[139,146],"above":[140],"both":[141],"floors":[142],"drops":[145],"as":[147,149],"soon":[148],"$v>V$;":[150],"if":[151],"control":[153],"also":[155],"purely":[156],"local":[157],"$\u03ba_3^2/(9V^2)>\u03ba_4/(12V)$,":[159],"drop":[161],"square-root":[164],"profile,":[165,174],"in":[167,224],"remaining":[169],"case":[171],"cube-root":[173],"derivative":[176],"$-\\infty$":[177],"way.":[181],"We":[182],"then":[183],"characterise":[184],"when":[185,200],"optimised":[187],"reproduces":[189],"Chernoff":[192],"deviation:":[193],"equality":[194],"holds":[195],"level":[198],"exactly":[199],"some":[201],"tangent":[207],"cumulant":[210],"Legendre":[215],"maximiser":[216],"for":[217,234],"level.":[219],"At":[220],"levels":[222],"tabulated":[223],"worked":[226],"example":[227],"$v=V$":[228],"costs":[229],"four":[230],"thirty":[232],"percent;":[233],"exponential":[237],"gap":[239],"persists":[240],"every":[242],"level,":[243],"reaching":[244],"thirteen":[245],"percent.":[246]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}