{"id":"https://openalex.org/W7215101012","doi":"https://doi.org/10.48550/arxiv.2609.38295","title":"A dimension-free bound for isoperimetry of unconditional log-concave measures","display_name":"A dimension-free bound for isoperimetry of unconditional log-concave measures","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7215101012","doi":"https://doi.org/10.48550/arxiv.2609.38295"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.38295","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38295","pdf_url":"https://arxiv.org/pdf/2609.38295","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/2609.38295","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086897744","display_name":"Dan Mikulincer","orcid":"https://orcid.org/0000-0003-3597-3550","observed_orcids":["https://orcid.org/0000-0003-3597-3550"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mikulincer, Dan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061028424","display_name":"Ilias Zadik","orcid":"https://orcid.org/0009-0008-4085-324X","observed_orcids":["https://orcid.org/0009-0008-4085-324X","https://orcid.org/0000-0002-8286-881X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zadik, Ilias","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":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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.8208000063896179,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.8208000063896179,"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":0.07069999724626541,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.044199999421834946,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/isoperimetry","display_name":"isoperimetry","score":0.8140000104904175},{"id":"https://openalex.org/keywords/poincare-inequality","display_name":"Poincar\u00e9 inequality","score":0.9259999990463257},{"id":"https://openalex.org/keywords/dimension-free-bounds","display_name":"dimension-free bounds","score":0.8140000104904175},{"id":"https://openalex.org/keywords/dunkl-operators","display_name":"Dunkl operators","score":0.8389999866485596},{"id":"https://openalex.org/keywords/spectral-analysis","display_name":"spectral analysis","score":0.9599999785423279}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7383999824523926},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.61080002784729},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6017000079154968},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.4975999891757965},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4092000126838684},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.38589999079704285},{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.37959998846054077},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.3125},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2653000056743622},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.259799987077713}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.38295","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38295","pdf_url":"https://arxiv.org/pdf/2609.38295","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.2609.38295","doi":"https://doi.org/10.48550/arxiv.2609.38295","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.38295","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:2609.38295","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38295","pdf_url":"https://arxiv.org/pdf/2609.38295","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/W7215101012.pdf","grobid_xml":"https://content.openalex.org/works/W7215101012.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7221020516","https://openalex.org/W1966782631","https://openalex.org/W1972250857","https://openalex.org/W1501178284","https://openalex.org/W6910627158","https://openalex.org/W7214928649","https://openalex.org/W4298304734","https://openalex.org/W2496348922","https://openalex.org/W7160257823","https://openalex.org/W4206361222"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,24,45,50],"dimension-free":[3],"Poincar\u00e9":[4],"inequality":[5],"for":[6],"isotropic":[7],"unconditional":[8,19],"log-concave":[9,38],"probability":[10],"measures,":[11],"establishing":[12],"the":[13,18,37,41,56,63,74,84],"Kannan-Lov\u00e1sz-Simonovits":[14],"(KLS)":[15],"conjecture":[16],"in":[17],"setting.":[20],"The":[21,59,79],"proof":[22,42,64],"combines":[23],"new":[25,51],"application":[26],"of":[27,36,49,62],"Dunkl":[28],"operator":[29,53],"theory":[30],"combined":[31],"with":[32,73],"an":[33],"appropriate":[34],"transformation":[35],"measure.":[39,58],"Specifically,":[40],"follows":[43],"by":[44,67],"direct":[46],"spectral":[47],"analysis":[48],"Dunkl-Langevin":[52],"adapted":[54],"to":[55],"transformed":[57],"core":[60],"ideas":[61],"were":[65],"generated":[66],"AI":[68],"generative":[69],"tools":[70],"through":[71],"interactions":[72],"authors":[75,80],"over":[76],"several":[77],"weeks.":[78],"refined":[81],"and":[82],"formalized":[83],"argument.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-10-02T00:00:00"}
