{"id":"https://openalex.org/W4406035356","doi":"https://doi.org/10.3390/e27010033","title":"On the Convergence Rate for the Longest at Most T-Contaminated Runs of Heads","display_name":"On the Convergence Rate for the Longest at Most T-Contaminated Runs of Heads","publication_year":2025,"publication_date":"2025-01-03","ids":{"openalex":"https://openalex.org/W4406035356","doi":"https://doi.org/10.3390/e27010033","pmid":"https://pubmed.ncbi.nlm.nih.gov/39851653"},"language":"en","primary_location":{"id":"doi:10.3390/e27010033","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27010033","pdf_url":"https://www.mdpi.com/1099-4300/27/1/33/pdf?version=1735897682","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/1/33/pdf?version=1735897682","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102804679","display_name":"Istv\u00e1n Fazekas","orcid":"https://orcid.org/0000-0001-9934-2972"},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Istv\u00e1n Fazekas","raw_affiliation_strings":["Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary"],"affiliations":[{"raw_affiliation_string":"Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045983072","display_name":"Borb\u00e1la Fazekas","orcid":null},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Borb\u00e1la Fazekas","raw_affiliation_strings":["Institute of Mathematics, University of Debrecen, Egyetem Square 1, 4032 Debrecen, Hungary"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Debrecen, Egyetem Square 1, 4032 Debrecen, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087127078","display_name":"L\u00e1szl\u00f3 F\u00f3ri\u00e1n","orcid":null},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 F\u00f3ri\u00e1n","raw_affiliation_strings":["Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary"],"affiliations":[{"raw_affiliation_string":"Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary","institution_ids":["https://openalex.org/I132735039"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102804679"],"corresponding_institution_ids":["https://openalex.org/I132735039"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0012039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","first_page":"33","last_page":"33"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14319","display_name":"Currency Recognition and Detection","score":0.6875,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T14319","display_name":"Currency Recognition and Detection","score":0.6875,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/coin-flipping","display_name":"Coin flipping","score":0.6365258693695068},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5196481943130493},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4596647024154663},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44283345341682434},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4391288161277771},{"id":"https://openalex.org/keywords/contamination","display_name":"Contamination","score":0.43685173988342285},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39849400520324707},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.29035383462905884},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06401059031486511}],"concepts":[{"id":"https://openalex.org/C97399411","wikidata":"https://www.wikidata.org/wiki/Q825367","display_name":"Coin flipping","level":2,"score":0.6365258693695068},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5196481943130493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4596647024154663},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44283345341682434},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4391288161277771},{"id":"https://openalex.org/C112570922","wikidata":"https://www.wikidata.org/wiki/Q60528603","display_name":"Contamination","level":2,"score":0.43685173988342285},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39849400520324707},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.29035383462905884},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06401059031486511},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e27010033","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27010033","pdf_url":"https://www.mdpi.com/1099-4300/27/1/33/pdf?version=1735897682","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:39851653","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39851653","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11765223","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11765223","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11765223/pdf/entropy-27-00033.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:f58e1649b50e4704816302eff2ed607c","is_oa":true,"landing_page_url":"https://doaj.org/article/f58e1649b50e4704816302eff2ed607c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 1, p 33 (2025)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/27/1/33/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e27010033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27010033","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27010033","pdf_url":"https://www.mdpi.com/1099-4300/27/1/33/pdf?version=1735897682","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406035356.pdf","grobid_xml":"https://content.openalex.org/works/W4406035356.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2013953286","https://openalex.org/W2053013517","https://openalex.org/W2153645832","https://openalex.org/W2329657751","https://openalex.org/W2737152433","https://openalex.org/W4391134178","https://openalex.org/W6659397386"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2074833159","https://openalex.org/W2022413236","https://openalex.org/W2915071022","https://openalex.org/W1647416393","https://openalex.org/W2895888930","https://openalex.org/W1618449339","https://openalex.org/W4246525302","https://openalex.org/W2083226356","https://openalex.org/W1856092221"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,26,29,32,45],"usual":[6],"coin":[7],"tossing":[8],"experiment.":[9],"We":[10,24,38],"call":[11],"a":[12,40],"run":[13],"at":[14,20,34],"most":[15,21,35],"<i>T</i>-contaminated,":[16],"if":[17],"it":[18],"contains":[19],"<i>T</i>":[22],"tails.":[23],"approximate":[25],"distribution":[27],"of":[28,31],"length":[30],"longest":[33],"<i>T</i>-contaminated":[36],"runs.":[37],"offer":[39],"more":[41],"precise":[42],"approximation":[43],"than":[44],"previous":[46],"one.":[47]},"counts_by_year":[],"updated_date":"2026-03-14T06:41:57.775601","created_date":"2025-10-10T00:00:00"}