{"id":"https://openalex.org/W4405283629","doi":"https://doi.org/10.3390/e26121082","title":"Some Open Questions About the Anisotropic Random Walks","display_name":"Some Open Questions About the Anisotropic Random Walks","publication_year":2024,"publication_date":"2024-12-11","ids":{"openalex":"https://openalex.org/W4405283629","doi":"https://doi.org/10.3390/e26121082","pmid":"https://pubmed.ncbi.nlm.nih.gov/39766711"},"language":"en","primary_location":{"id":"doi:10.3390/e26121082","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121082","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1082/pdf?version=1733931085","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/1099-4300/26/12/1082/pdf?version=1733931085","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022975781","display_name":"Endre Cs\u00e1ki","orcid":"https://orcid.org/0000-0002-9120-6201"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Endre Cs\u00e1ki","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, P.O. Box 127, H-1364 Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, P.O. Box 127, H-1364 Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015587881","display_name":"Ant\u00f3nia F\u00f6ldes","orcid":"https://orcid.org/0000-0002-6036-2607"},"institutions":[{"id":"https://openalex.org/I142393192","display_name":"College of Staten Island","ror":"https://ror.org/02p179j44","country_code":"US","type":"education","lineage":["https://openalex.org/I142393192"]},{"id":"https://openalex.org/I174216632","display_name":"City University of New York","ror":"https://ror.org/00453a208","country_code":"US","type":"education","lineage":["https://openalex.org/I174216632"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ant\u00f3nia F\u00f6ldes","raw_affiliation_strings":["Department of Mathematics, College of Staten Island, The City University of New York, 2800 Victory Blvd., Staten Island, NY 10314, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Staten Island, The City University of New York, 2800 Victory Blvd., Staten Island, NY 10314, USA","institution_ids":["https://openalex.org/I142393192","https://openalex.org/I174216632"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015587881"],"corresponding_institution_ids":["https://openalex.org/I142393192","https://openalex.org/I174216632"],"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":0.22522656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"12","first_page":"1082","last_page":"1082"},"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":0.9954000115394592,"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":0.9954000115394592,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9919999837875366,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9763000011444092,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/dozen","display_name":"Dozen","score":0.8090962171554565},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5625057816505432},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.5456136465072632},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49310633540153503},{"id":"https://openalex.org/keywords/data-science","display_name":"Data science","score":0.4026636779308319},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.384110689163208},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3272077441215515},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2815186381340027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2699436545372009},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19845083355903625},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.09603151679039001}],"concepts":[{"id":"https://openalex.org/C185181809","wikidata":"https://www.wikidata.org/wiki/Q605704","display_name":"Dozen","level":2,"score":0.8090962171554565},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5625057816505432},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5456136465072632},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49310633540153503},{"id":"https://openalex.org/C2522767166","wikidata":"https://www.wikidata.org/wiki/Q2374463","display_name":"Data science","level":1,"score":0.4026636779308319},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.384110689163208},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3272077441215515},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2815186381340027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2699436545372009},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19845083355903625},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.09603151679039001},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26121082","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121082","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1082/pdf?version=1733931085","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:39766711","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39766711","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:11675976","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11675976","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11675976/pdf/entropy-26-01082.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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:e0e7cd35825f41928f1e702d4c9a3bc1","is_oa":false,"landing_page_url":"https://doaj.org/article/e0e7cd35825f41928f1e702d4c9a3bc1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 12, p 1082 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26121082","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121082","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1082/pdf?version=1733931085","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/W4405283629.pdf","grobid_xml":"https://content.openalex.org/works/W4405283629.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W111585255","https://openalex.org/W269033978","https://openalex.org/W1566428193","https://openalex.org/W1983976275","https://openalex.org/W1987299262","https://openalex.org/W1988117979","https://openalex.org/W2008594757","https://openalex.org/W2009523665","https://openalex.org/W2012451562","https://openalex.org/W2025038670","https://openalex.org/W2026690703","https://openalex.org/W2027445645","https://openalex.org/W2033844009","https://openalex.org/W2038245900","https://openalex.org/W2039828603","https://openalex.org/W2049644680","https://openalex.org/W2056913373","https://openalex.org/W2058506279","https://openalex.org/W2061563753","https://openalex.org/W2063656727","https://openalex.org/W2083269317","https://openalex.org/W2090240571","https://openalex.org/W2099492883","https://openalex.org/W2139501386","https://openalex.org/W2160503600","https://openalex.org/W2167306696","https://openalex.org/W2315956236","https://openalex.org/W2507770748","https://openalex.org/W2625580452","https://openalex.org/W2971246174","https://openalex.org/W3121169013","https://openalex.org/W4226375041","https://openalex.org/W4283771926","https://openalex.org/W4301487029","https://openalex.org/W4388038337","https://openalex.org/W6640971972","https://openalex.org/W6681507942"],"related_works":["https://openalex.org/W4232622239","https://openalex.org/W4248098561","https://openalex.org/W4392840857","https://openalex.org/W2809019971","https://openalex.org/W2145289172","https://openalex.org/W2089830040","https://openalex.org/W4230509584","https://openalex.org/W2793725298","https://openalex.org/W1984231369","https://openalex.org/W2044358132"],"abstract_inverted_index":{"Between":[0],"2007":[1],"and":[2,10,34],"2018,":[3],"we":[4,27,36],"collaborated":[5],"extensively":[6],"with":[7],"P\u00e1l":[8],"R\u00e9v\u00e9sz":[9],"Mikl\u00f3s":[11],"Cs\u00f6rg\u0151":[12],"on":[13],"many":[14],"of":[15,39,56],"the":[16,23,40,61],"problems":[17],"discussed":[18],"in":[19,45],"this":[20],"paper.":[21],"Over":[22],"past":[24],"six":[25],"years,":[26],"have":[28],"continued":[29],"to":[30,64],"explore":[31],"these":[32,46,66],"issues,":[33],"here,":[35],"present":[37],"some":[38],"most":[41],"intriguing":[42],"open":[43],"questions":[44],"areas.":[47],"This":[48],"paper":[49],"compiles":[50],"key":[51],"results":[52],"from":[53],"a":[54],"dozen":[55],"our":[57],"previous":[58],"works,":[59],"providing":[60],"necessary":[62],"background":[63],"frame":[65],"compelling":[67],"unresolved":[68],"questions.":[69]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
