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Catalan Numbers and Free Distributions of Mutually Free Multi Semicircular Elements

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Abstract

In this paper, we consider certain relations among Catalan numbers, and study free distributions of mutually free, multi semicircular elements. We not only characterize the joint free distributions of given multi semicircular elements, but also provide estimations for such free-distributional data by using our relations among Catalan numbers. As application, asymptotic behaviors of the joint free distribution of mutually free, multi semicircular elements are considered.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, St. Ambrose University, 421 Ambrose Hall, 518 W. Locust Street, Davenport, IA, 52803, USA

    Ilwoo Cho

  2. Department of Mathematics and Statistics, St. Ambrose University, 418 Ambrose Hall, 518 W. Lucust Street, Davenport, IA, 52803, USA

    Junyi Dong

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  1. Ilwoo Cho
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  2. Junyi Dong
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Correspondence to Ilwoo Cho.

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Communicated by Daniel Alpay.

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This article is part of the topical collection “Infinite-dimensional Analysis and Non-commutative Theory” edited by Marek Bozejko, Palle Jorgensen and Yuri Kondratiev.

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Cho, I., Dong, J. Catalan Numbers and Free Distributions of Mutually Free Multi Semicircular Elements. Complex Anal. Oper. Theory 18, 23 (2024). https://doi.org/10.1007/s11785-023-01452-7

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  • DOI: https://doi.org/10.1007/s11785-023-01452-7

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