{"id":"https://openalex.org/W4415198643","doi":"https://doi.org/10.4230/lipics.approx/random.2025.44","title":"Density Frankl-R\u00f6dl on the Sphere","display_name":"Density Frankl-R\u00f6dl on the Sphere","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4415198643","doi":"https://doi.org/10.4230/lipics.approx/random.2025.44"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.09839","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.09839","pdf_url":"https://arxiv.org/pdf/2505.09839","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"article","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.09839","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120005000","display_name":"Venkatesan Guruswami","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Guruswami, Venkatesan","raw_affiliation_strings":["Department of EECS, University of California, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7926-3396","affiliations":[{"raw_affiliation_string":"Department of EECS, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052553875","display_name":"Shilun Li","orcid":"https://orcid.org/0000-0001-5765-0432"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Li, Shilun","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-5765-0432","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5120005000"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.34692875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.958899974822998,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.958899974822998,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9325000047683716,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9283999800682068,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7803000211715698},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5629000067710876},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5145999789237976},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.39070001244544983},{"id":"https://openalex.org/keywords/inner-product-space","display_name":"Inner product space","score":0.3659999966621399}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7803000211715698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6761999726295471},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5629000067710876},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5145999789237976},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.375},{"id":"https://openalex.org/C91855343","wikidata":"https://www.wikidata.org/wiki/Q214159","display_name":"Inner product space","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3149000108242035},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2989000082015991},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2768000066280365}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2505.09839","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.09839","pdf_url":"https://arxiv.org/pdf/2505.09839","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2505.09839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.09839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.4230/lipics.approx/random.2025.44","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.approx/random.2025.44","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2505.09839","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.09839","pdf_url":"https://arxiv.org/pdf/2505.09839","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"establish":[1,32],"a":[2,20,25,39,49,62,85,107],"density":[3,63,111],"variant":[4],"of":[5,17,43,55,65,87,109],"the":[6,10,36],"Frankl-R\u00f6dl":[7],"theorem":[8],"on":[9,35],"sphere":[11,120],"$\\mathbb{S}^{n-1}$,":[12],"which":[13,69,93],"concerns":[14],"avoiding":[15],"pairs":[16],"vectors":[18,45],"with":[19,77,96],"specific":[21],"distance,":[22],"or":[23],"equivalently,":[24],"prescribed":[26,78,98],"inner":[27,80,99],"product.":[28],"In":[29],"particular,":[30],"we":[31,60,89,113],"lower":[33],"bounds":[34],"probability":[37],"that":[38,115],"randomly":[40],"chosen":[41],"pair":[42],"such":[44],"lies":[46],"entirely":[47],"within":[48],"measurable":[50],"subset":[51],"$A":[52],"\\subseteq":[53],"\\mathbb{S}^{n-1}$":[54],"sufficiently":[56],"large":[57],"measure.":[58],"Additionally,":[59],"prove":[61],"version":[64],"spherical":[66],"avoidance":[67,73],"problems,":[68],"generalize":[70],"from":[71],"pairwise":[72,79],"to":[74],"broader":[75],"configurations":[76,88,118],"products.":[81],"Our":[82],"framework":[83],"encompasses":[84],"class":[86],"call":[90],"inductive":[91,117],"configurations,":[92],"include":[94],"simplices":[95],"any":[97],"product":[100],"$-1":[101],"&lt;":[102,104],"r":[103],"1$.":[105],"As":[106],"consequence":[108],"our":[110],"statement,":[112],"show":[114],"all":[116],"are":[119],"Ramsey.":[121]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-15T00:00:00"}
