{"id":"https://openalex.org/W7220992265","doi":"https://doi.org/10.48550/arxiv.2610.07876","title":"A very short proof of the subgaussian convex-order comparison theorem","display_name":"A very short proof of the subgaussian convex-order comparison theorem","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220992265","doi":"https://doi.org/10.48550/arxiv.2610.07876"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07876","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07876","pdf_url":"https://arxiv.org/pdf/2610.07876","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/2610.07876","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041943056","display_name":"Antoine Song","orcid":"https://orcid.org/0000-0001-8285-6627","observed_orcids":["https://orcid.org/0000-0001-8285-6627"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Song, Antoine","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077443351","display_name":"Michel Talagrand","orcid":"https://orcid.org/0000-0003-4956-3966","observed_orcids":["https://orcid.org/0000-0003-4956-3966"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Talagrand, Michel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T13500","display_name":"Probability and Statistical Research","score":0.5443999767303467,"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":0.5443999767303467,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.1071000024676323,"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/T11716","display_name":"Random Matrices and Applications","score":0.08980000019073486,"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":0.8460000157356262},{"id":"https://openalex.org/keywords/comparison-theorems","display_name":"comparison theorems","score":0.6869999766349792},{"id":"https://openalex.org/keywords/gaussian-random-vectors","display_name":"Gaussian random vectors","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6658999919891357},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4912000000476837},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4293999969959259},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4115000069141388},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3336000144481659},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3149000108242035},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2531999945640564},{"id":"https://openalex.org/C2986577269","wikidata":"https://www.wikidata.org/wiki/Q11306265","display_name":"Random noise","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07876","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07876","pdf_url":"https://arxiv.org/pdf/2610.07876","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.2610.07876","doi":"https://doi.org/10.48550/arxiv.2610.07876","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07876","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:2610.07876","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07876","pdf_url":"https://arxiv.org/pdf/2610.07876","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/W7220992265.pdf","grobid_xml":"https://content.openalex.org/works/W7220992265.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W46152070","https://openalex.org/W1555319958","https://openalex.org/W2081780258","https://openalex.org/W2532991447","https://openalex.org/W7077901576","https://openalex.org/W7117117144","https://openalex.org/W7150943614","https://openalex.org/W7158557735","https://openalex.org/W7160900955"],"related_works":["https://openalex.org/W7117117144","https://openalex.org/W7158557735","https://openalex.org/W7150943614","https://openalex.org/W7160900955","https://openalex.org/W7207592338","https://openalex.org/W7131849614","https://openalex.org/W2914234208","https://openalex.org/W2048733769","https://openalex.org/W4403362538","https://openalex.org/W7065834802"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2,30,34],"very":[3],"short":[4],"proof":[5],"of":[6],"the":[7],"following":[8],"comparison":[9],"theorem,":[10],"which":[11],"has":[12],"recently":[13],"played":[14],"an":[15],"important":[16],"role:":[17],"every":[18],"centered":[19],"subgaussian":[20],"random":[21,37],"vector":[22],"is":[23],"dominated":[24],"in":[25],"convex":[26],"order,":[27],"up":[28],"to":[29],"universal":[31],"constant,":[32],"by":[33],"standard":[35],"Gaussian":[36],"vector.":[38]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
