{"id":"https://openalex.org/W4377138065","doi":"https://doi.org/10.37236/11600","title":"The Park-Pham Theorem with Optimal Convergence Rate","display_name":"The Park-Pham Theorem with Optimal Convergence Rate","publication_year":2023,"publication_date":"2023-05-19","ids":{"openalex":"https://openalex.org/W4377138065","doi":"https://doi.org/10.37236/11600"},"language":"en","primary_location":{"id":"doi:10.37236/11600","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11600","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p25/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046539223","display_name":"Tolson Bell","orcid":"https://orcid.org/0000-0003-0956-6265"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tolson Bell","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046539223"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.6616,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.70131354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"30","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994000196456909,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994000196456909,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973000288009644,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.853929877281189},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7609165906906128},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6500347852706909},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6437204480171204},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.6357775926589966},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5416903495788574},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.48667293787002563},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46919628977775574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45076096057891846},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.44403499364852905},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12749361991882324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12134072184562683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.853929877281189},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7609165906906128},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6500347852706909},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6437204480171204},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.6357775926589966},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5416903495788574},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.48667293787002563},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46919628977775574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45076096057891846},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.44403499364852905},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12749361991882324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12134072184562683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/11600","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11600","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/11600","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11600","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3313328687","display_name":null,"funder_award_id":"DGE 2140739","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4377138065.pdf"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1991001643","https://openalex.org/W2081780258","https://openalex.org/W2982592370","https://openalex.org/W3195642419","https://openalex.org/W3212605836","https://openalex.org/W4297166567","https://openalex.org/W4385899778","https://openalex.org/W6766699743","https://openalex.org/W6783235256","https://openalex.org/W6843704251"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W1630514295","https://openalex.org/W1537073411","https://openalex.org/W2963081352","https://openalex.org/W4376608938","https://openalex.org/W4288275998","https://openalex.org/W2472555608","https://openalex.org/W4214498971"],"abstract_inverted_index":{"Park":[0],"and":[1,18],"Pham's":[2],"recent":[3],"proof":[4],"of":[5,16,39,81],"the":[6,14,28,65,82],"Kahn-Kalai":[7],"conjecture":[8],"was":[9],"a":[10,32,36,41,79],"major":[11],"breakthrough":[12],"in":[13,48],"field":[15],"graph":[17],"hypergraph":[19],"thresholds.":[20],"Their":[21],"result":[22],"gives":[23],"an":[24],"upper":[25],"bound":[26,47],"on":[27,68],"threshold":[29],"at":[30],"which":[31],"probabilistic":[33],"construction":[34],"has":[35],"$1-\\epsilon$":[37],"chance":[38],"achieving":[40],"given":[42],"monotone":[43],"property.":[44],"While":[45],"their":[46],"other":[49],"parameters":[50],"is":[51],"optimal":[52,66,86],"up":[53],"to":[54],"constant":[55],"factors":[56],"for":[57],"any":[58],"fixed":[59],"$\\epsilon$,":[60],"it":[61],"does":[62],"not":[63],"have":[64],"dependence":[67],"$\\epsilon$":[69],"as":[70],"$\\epsilon\\rightarrow":[71],"0$.":[72],"In":[73],"this":[74],"short":[75],"paper,":[76],"we":[77],"prove":[78],"version":[80],"Park-Pham":[83],"Theorem":[84],"with":[85],"$\\epsilon$-dependence.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}