{"id":"https://openalex.org/W7204209884","doi":"https://doi.org/10.48550/arxiv.2608.21663","title":"Variance lower bounds for geometric functionals of rotationally invariant log-concave random polytopes","display_name":"Variance lower bounds for geometric functionals of rotationally invariant log-concave random polytopes","publication_year":2026,"publication_date":"2026-08-21","ids":{"openalex":"https://openalex.org/W7204209884","doi":"https://doi.org/10.48550/arxiv.2608.21663"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.21663","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21663","pdf_url":"https://arxiv.org/pdf/2608.21663","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/2608.21663","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081092413","display_name":"Minas Pafis","orcid":"https://orcid.org/0009-0002-0600-5075","observed_orcids":["https://orcid.org/0009-0002-0600-5075"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pafis, Minas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124028477","display_name":"Christos Pandis","orcid":"https://orcid.org/0009-0001-0512-4657","observed_orcids":["https://orcid.org/0009-0001-0512-4657"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pandis, Christos","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/T11830","display_name":"Point processes and geometric inequalities","score":1.0,"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/T11830","display_name":"Point processes and geometric inequalities","score":1.0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/variance-lower-bound","display_name":"variance lower bound","score":0.890999972820282},{"id":"https://openalex.org/keywords/random-polytopes","display_name":"random polytopes","score":0.9570000171661377},{"id":"https://openalex.org/keywords/intrinsic-volumes","display_name":"intrinsic volumes","score":0.9940000176429749},{"id":"https://openalex.org/keywords/face-numbers","display_name":"face numbers","score":0.9929999709129333},{"id":"https://openalex.org/keywords/geometric-functionals","display_name":"geometric functionals","score":0.7350000143051147},{"id":"https://openalex.org/keywords/barycentric-coordinates","display_name":"barycentric coordinates","score":0.9649999737739563},{"id":"https://openalex.org/keywords/convex-hull","display_name":"convex hull","score":0.46799999475479126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7785999774932861},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7483999729156494},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.6158000230789185},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5831000208854675},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5468999743461609},{"id":"https://openalex.org/C7605037","wikidata":"https://www.wikidata.org/wiki/Q327164","display_name":"Geometric probability","level":2,"score":0.5284000039100647},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47940000891685486},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4011000096797943},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.39410001039505005},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C62100291","wikidata":"https://www.wikidata.org/wiki/Q1936288","display_name":"Total variation","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3424000144004822},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C2985420695","wikidata":"https://www.wikidata.org/wiki/Q175199","display_name":"Population variance","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2833000123500824},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2669000029563904}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.21663","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21663","pdf_url":"https://arxiv.org/pdf/2608.21663","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.2608.21663","doi":"https://doi.org/10.48550/arxiv.2608.21663","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.21663","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:2608.21663","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21663","pdf_url":"https://arxiv.org/pdf/2608.21663","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204209884.pdf","grobid_xml":"https://content.openalex.org/works/W7204209884.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4417024181"],"related_works":["https://openalex.org/W2594481626","https://openalex.org/W4417024181","https://openalex.org/W4252679200","https://openalex.org/W2081680874","https://openalex.org/W2045924955","https://openalex.org/W2625719118","https://openalex.org/W2466333554","https://openalex.org/W7096536991","https://openalex.org/W7204544114","https://openalex.org/W7100347786"],"abstract_inverted_index":{"We":[0,77],"establish":[1],"variance":[2,82],"lower":[3,37],"bounds":[4,38],"for":[5,66,84],"the":[6,10,34,58,89],"intrinsic":[7,86],"volumes":[8,87],"and":[9,41,43,46,64,88],"face":[11],"numbers":[12],"of":[13,39,44,52,91],"random":[14],"polytopes,":[15],"generated":[16],"by":[17,62],"independent":[18],"samples":[19],"from":[20],"rotationally":[21],"invariant":[22],"log-concave":[23],"probability":[24],"measures":[25],"on":[26,57,74],"$\\mathbb{R}^d$":[27],"with":[28,80],"full":[29],"support.":[30],"Our":[31,54],"results":[32],"extend":[33],"corresponding":[35],"Gaussian":[36],"B\u00e1r\u00e1ny":[40,45,63],"Vu":[42],"Th\u00e4le":[47],"to":[48],"this":[49],"broader":[50],"class":[51],"distributions.":[53],"proof":[55],"builds":[56],"geometric":[59],"construction":[60],"introduced":[61],"Vu,":[65],"which":[67],"we":[68],"develop":[69],"an":[70],"alternative":[71],"treatment":[72],"based":[73],"barycentric":[75],"coordinates.":[76],"combine":[78],"it":[79],"local":[81],"estimates":[83],"both":[85],"number":[90],"faces.":[92]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-26T00:00:00"}
