{"id":"https://openalex.org/W4382626738","doi":"https://doi.org/10.3390/sym15051046","title":"Two-Dimensional Moran Model","display_name":"Two-Dimensional Moran Model","publication_year":2023,"publication_date":"2023-05-09","ids":{"openalex":"https://openalex.org/W4382626738","doi":"https://doi.org/10.3390/sym15051046"},"language":"en","primary_location":{"id":"doi:10.3390/sym15051046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051046","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1046/pdf?version=1683607026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/5/1046/pdf?version=1683607026","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042517033","display_name":"Asma Althagafi","orcid":null},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Asma Althagafi","raw_affiliation_strings":["Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016425203","display_name":"Mohamed Abdelkader","orcid":"https://orcid.org/0000-0001-5660-555X"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohamed Abdelkader","raw_affiliation_strings":["Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042517033"],"corresponding_institution_ids":["https://openalex.org/I28022161"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.1442,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.85833077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"15","issue":"5","first_page":"1046","last_page":"1046"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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":0.9976999759674072,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9970999956130981,"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/mathematics","display_name":"Mathematics","score":0.5253909230232239},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.4851716160774231},{"id":"https://openalex.org/keywords/reset","display_name":"Reset (finance)","score":0.4688583016395569},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45005133748054504},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.44563955068588257},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.43999195098876953},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.43189725279808044},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.4236024022102356},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32600757479667664},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.29935717582702637},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23370516300201416},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16794532537460327}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5253909230232239},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.4851716160774231},{"id":"https://openalex.org/C2779795794","wikidata":"https://www.wikidata.org/wiki/Q7315343","display_name":"Reset (finance)","level":2,"score":0.4688583016395569},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45005133748054504},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.44563955068588257},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.43999195098876953},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.43189725279808044},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4236024022102356},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32600757479667664},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.29935717582702637},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23370516300201416},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16794532537460327},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15051046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051046","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1046/pdf?version=1683607026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1878e2fec1e54febb192ff6937a58ffc","is_oa":true,"landing_page_url":"https://doaj.org/article/1878e2fec1e54febb192ff6937a58ffc","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":"Symmetry, Vol 15, Iss 5, p 1046 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/5/1046/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15051046","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15051046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051046","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1046/pdf?version=1683607026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.46000000834465027,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382626738.pdf","grobid_xml":"https://content.openalex.org/works/W4382626738.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W186403072","https://openalex.org/W1558729961","https://openalex.org/W1906132287","https://openalex.org/W2010100934","https://openalex.org/W2035426885","https://openalex.org/W2036411820","https://openalex.org/W2043748383","https://openalex.org/W2084079228","https://openalex.org/W2098828803","https://openalex.org/W2140083166","https://openalex.org/W2484540864","https://openalex.org/W2962927968","https://openalex.org/W4323537117","https://openalex.org/W6652741265","https://openalex.org/W6739478401"],"related_works":["https://openalex.org/W350273603","https://openalex.org/W2393495588","https://openalex.org/W96259911","https://openalex.org/W2168225754","https://openalex.org/W4385608460","https://openalex.org/W2370772865","https://openalex.org/W1528611913","https://openalex.org/W2000034628","https://openalex.org/W2387487224","https://openalex.org/W4366146733"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,58],"consider":[4],"a":[5,53],"two-dimensional":[6],"Moran":[7],"model":[8],"of":[9,13,24,39,49,62],"random":[10],"walks":[11],"consisting":[12],"two":[14,64],"queues":[15],"evolving":[16],"in":[17],"parallel":[18],"which":[19],"can":[20],"(at":[21],"each":[22,50],"unit":[23],"time)":[25],"either":[26],"increase":[27],"by":[28],"one":[29],"or":[30],"reset":[31],"to":[32],"0.":[33],"We":[34],"analyze":[35,59],"the":[36,46,60,71],"joint":[37],"law":[38],"their":[40],"final":[41],"altitude":[42],"and":[43,57,73],"prove":[44],"that":[45],"asymptotic":[47],"distribution":[48,56],"component":[51],"is":[52],"shifted":[54],"geometric":[55],"maximum":[61],"these":[63],"components,":[65],"also":[66],"giving":[67],"closed":[68],"forms":[69],"for":[70],"mean":[72],"variance.":[74]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}