{"id":"https://openalex.org/W7161065337","doi":"https://doi.org/10.48550/arxiv.2605.11451","title":"Convex order under majorization for projections of ell-p balls","display_name":"Convex order under majorization for projections of ell-p balls","publication_year":2026,"publication_date":"2026-05-12","ids":{"openalex":"https://openalex.org/W7161065337","doi":"https://doi.org/10.48550/arxiv.2605.11451"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.11451","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.11451","pdf_url":"https://arxiv.org/pdf/2605.11451","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":"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/2605.11451","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128525403","display_name":"Soufiane Fafe","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fafe, Soufiane","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5128525403"],"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9047999978065491,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9047999978065491,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.07530000060796738,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.01269999984651804,"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/convex-order","display_name":"convex order","score":0.949999988079071},{"id":"https://openalex.org/keywords/majorization","display_name":"majorization","score":0.9909999966621399},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.9399999976158142},{"id":"https://openalex.org/keywords/schur-convexity","display_name":"Schur convexity","score":0.8339999914169312},{"id":"https://openalex.org/keywords/central-sections","display_name":"central sections","score":0.3630000054836273},{"id":"https://openalex.org/keywords/moment-inequalities","display_name":"moment inequalities","score":0.5479999780654907},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7749999761581421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8260999917984009},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6265000104904175},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5928999781608582},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5733000040054321},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5717999935150146},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5231000185012817},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.4657000005245209},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.45750001072883606},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4104999899864197},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.38100001215934753},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35850000381469727},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3531000018119812},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C2780639617","wikidata":"https://www.wikidata.org/wiki/Q6516972","display_name":"Quadrant (abdomen)","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.2700999975204468},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.26100000739097595},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.25929999351501465},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.11451","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.11451","pdf_url":"https://arxiv.org/pdf/2605.11451","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2605.11451","doi":"https://doi.org/10.48550/arxiv.2605.11451","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.11451","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:2605.11451","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.11451","pdf_url":"https://arxiv.org/pdf/2605.11451","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":"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/W7161065337.pdf","grobid_xml":"https://content.openalex.org/works/W7161065337.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1972194652","https://openalex.org/W2107298062","https://openalex.org/W2808574218","https://openalex.org/W4307285540","https://openalex.org/W4383878498"],"related_works":["https://openalex.org/W7222978388","https://openalex.org/W1932856329","https://openalex.org/W3000733790","https://openalex.org/W2152196758","https://openalex.org/W4390540510","https://openalex.org/W4221141702","https://openalex.org/W2158763591","https://openalex.org/W2035715326","https://openalex.org/W7220937733","https://openalex.org/W7167574057"],"abstract_inverted_index":{"Let":[0],"$n\\ge1$":[1],"and":[2,5,68,118,136,165],"$1\\le":[3],"p\\le2$,":[4],"let":[6],"$X$":[7],"be":[8],"uniformly":[9],"distributed":[10],"on":[11,106],"the":[12,44,99,103,151],"unit":[13],"ball":[14],"$B_p^n$":[15],"of":[16,43,102,142],"$\\ell_p^n$.":[17],"We":[18],"prove":[19],"that":[20],"if":[21],"$(a_1^2,\\ldots,a_n^2)$":[22],"majorizes":[23],"$(b_1^2,\\ldots,b_n^2)$,":[24],"then":[25],"$\\langle":[26,31],"b,X\\rangle^2$":[27],"is":[28,110,148],"dominated":[29],"by":[30,55],"a,X\\rangle^2$":[32],"in":[33,150],"convex":[34],"order.":[35],"For":[36],"$p<2$":[37],"this":[38],"gives":[39],"a":[40,70,82,87,113,156,162,166],"nontrivial":[41],"comparison":[42,85,109],"complete":[45],"squared-projection":[46],"laws,":[47],"whereas":[48],"at":[49],"$p=2$":[50],"it":[51],"reduces":[52],"to":[53,121],"equality":[54],"rotational":[56],"invariance.":[57],"The":[58,108,146],"result":[59],"strengthens":[60],"known":[61],"majorization":[62,96],"inequalities":[63,131],"for":[64,74,90,132,154],"individual":[65],"power":[66],"moments":[67],"provides":[69],"single":[71],"distributional":[72],"source":[73],"several":[75],"familiar":[76],"projection":[77],"inequalities.":[78],"Its":[79],"proof":[80],"combines":[81],"two-dimensional":[83],"hinge-function":[84],"with":[86,124,140],"preservation":[88],"theorem":[89],"Beta--Rademacher":[91],"perturbations,":[92],"which":[93],"lifts":[94],"elementary":[95],"transfers":[97],"through":[98],"Dirichlet":[100],"representation":[101],"uniform":[104],"measure":[105],"$B_p^n$.":[107],"stable":[111],"under":[112],"common":[114],"independent":[115],"radial":[116,126],"scaling":[117],"therefore":[119],"extends":[120],"$\\ell_p$-radial":[122],"measures":[123],"nonincreasing":[125],"density.":[127],"Consequences":[128],"include":[129],"simultaneous":[130],"moments,":[133],"hinge":[134],"functions,":[135],"Laplace":[137],"transforms,":[138],"together":[139],"Schur-convexity":[141],"Gaussian-regularized":[143],"central-section":[144],"densities.":[145],"range":[147],"sharp":[149],"stated":[152],"direction:":[153],"$p>2$,":[155],"support":[157],"obstruction":[158],"already":[159],"occurs":[160],"between":[161],"coordinate":[163],"direction":[164],"two-coordinate":[167],"direction.":[168]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-05-14T00:00:00"}
