{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:07:56Z","timestamp":1760148476965,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T00:00:00Z","timestamp":1683590400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider a two-dimensional Moran model of random walks consisting of two queues evolving in parallel which can (at each unit of time) either increase by one or reset to 0. We analyze the joint law of their final altitude and prove that the asymptotic distribution of each component is a shifted geometric distribution and we analyze the maximum of these two components, also giving closed forms for the mean and variance.<\/jats:p>","DOI":"10.3390\/sym15051046","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T01:06:28Z","timestamp":1683594388000},"page":"1046","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Two-Dimensional Moran Model"],"prefix":"10.3390","volume":"15","author":[{"given":"Asma","family":"Althagafi","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5660-555X","authenticated-orcid":false,"given":"Mohamed","family":"Abdelkader","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,9]]},"reference":[{"key":"ref_1","first-page":"37","article-title":"Basic analytic combinatorics of directed lattice paths","volume":"281","author":"Banderier","year":"2002","journal-title":"Theor. 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Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1239\/jap\/1253279856","article-title":"Duality and asymptotics for a class of nonneutral discrete Moran models","volume":"46","author":"Huillet","year":"2009","journal-title":"J. Appl. Probab."},{"doi-asserted-by":"crossref","unstructured":"Cordero, F., and V\u00e9chambre, G. (2023). Moran models and Wright-Fisher diffusions with selection and mutation in a one-sided random environment. Adv. Appl. Probab., 1\u201367.","key":"ref_12","DOI":"10.1017\/apr.2022.54"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1080\/08898480.2015.1087775","article-title":"Random walk Green kernels in the neutral Moran model conditioned on survivors at a random time to origin","volume":"23","author":"Huillet","year":"2016","journal-title":"Math. Popul. Stud."},{"key":"ref_14","first-page":"135","article-title":"Approximating general discrete stochastic processes by Markov chains","volume":"1","year":"2022","journal-title":"J. Stat. Comput. Sci."},{"unstructured":"Althagafi, A., Aguech, R., and Banderier, C. (2023). Height of Walks with Resets and the Moran Model. submitted.","key":"ref_15"},{"unstructured":"Banderier, C. (2001). Combinatoire Analytique des Chemins et des Cartes. [Ph.D. Thesis, Universit\u00e9 Paris VI].","key":"ref_16"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1046\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:31:49Z","timestamp":1760124709000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,9]]},"references-count":16,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["sym15051046"],"URL":"https:\/\/doi.org\/10.3390\/sym15051046","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,5,9]]}}}