{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:43:32Z","timestamp":1760114612516,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T00:00:00Z","timestamp":1726617600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSPD2024R1068"],"award-info":[{"award-number":["RSPD2024R1068"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this current paper, we propose to study a three-dimensional Moran model (Xn(1),Xn(2),Xn(3)), where each random walk (Xn(i))\u2208{1,2,3} increases by one unit or is reset to zero at each unit of time. We analyze the joint law of its final altitude Xn=max(Xn(1),Xn(2),Xn(3)) via the moment generating tools. Furthermore, we show that the limit distribution of each random walk follows a shifted geometric distribution with parameter 1\u2212qi, and we analyze the maximum of these three walks, also giving explicit expressions for the mean and variance.<\/jats:p>","DOI":"10.3390\/sym16091222","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T09:43:13Z","timestamp":1726652593000},"page":"1222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Three-Dimensional Moran Walk with Resets"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5660-555X","authenticated-orcid":false,"given":"Mohamed","family":"Abdelkader","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,18]]},"reference":[{"key":"ref_1","unstructured":"Banderier, C. 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Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1017\/S0305004100033193","article-title":"Random processes in genetics","volume":"54","author":"Moran","year":"1958","journal-title":"Proc. Camb. Philos. Soc."},{"key":"ref_14","unstructured":"Moran, P.A.P. (1962). 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