{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T17:15:37Z","timestamp":1772212537120,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Deanship of Graduate Studies and Scientific Research at Jouf University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Several authors are interested in the study of limiting distributions for large symmetrical random matrices. Our approach of studying limiting distributions is different and is related to the new concept of variance functions of Cauchy\u2013Stieltjes Kernel (CSK) families of probabilities. By means of the variance functions machinery, some novel limiting probability measures are provided involving the free multiplicative law of large numbers, using both free and Boolean (additive and multiplicative) convolutions. Several examples of these limiting probability measures are given in the context of free probability.<\/jats:p>","DOI":"10.3390\/sym16101365","type":"journal-article","created":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T12:44:31Z","timestamp":1728909871000},"page":"1365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some Limiting Measures Related to Free and Boolean Convolutions"],"prefix":"10.3390","volume":"16","author":[{"given":"Ayed. R. A.","family":"Alanzi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}]},{"given":"Shokrya S.","family":"Alshqaq","sequence":"additional","affiliation":[{"name":"College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia"}]},{"given":"Raouf","family":"Fakhfakh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10959-013-0508-x","article-title":"Limiting Spectral Distribution of Large Sample Covariance Matrices Associated with a Class of Stationary Processes","volume":"28","author":"Banna","year":"2015","journal-title":"J. Theor. 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