Do, YenNguyen, Hoi HNguyen, OanhPritsker, Igor E2024-01-172024-01-172021-11-17Do, Y., Nguyen, H.H., Nguyen, O., Pritsker, I.E. (2021). Central Limit Theorem for the number of real roots of random orthogonal polynomials. https://doi.org/10.48550/arxiv.2111.09015https://hdl.handle.net/20.500.14446/340122In this note we study the number of real roots of a wide class of random orthogonal polynomials with gaussian coefficients. Using the method of Wiener Chaos we show that the fluctuation in the bulk is asymptotically gaussian, even when the local correlations are different.application/pdfThis material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information.2024-01-1610.48550/arxiv.2111.09015Preprintapplied mathematicsmathematical sciencesstatisticsORCID: 0000-0002-3102-5003 (Pritsker, Igor E)ScopusID: 6602900239 (Pritsker, Igor E)