On gegenbauer point processes on the unit interval

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URI: https://hdl.handle.net/10902/31926
ISSN: 0926-2601
ISSN: 1572-929X
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Autoría
Beltrán Álvarez, CarlosAutoridad Unican; Delgado, Antonia; Fernández, Lidia; Sánchez-Lara, Joaquín
Fecha
2024-01
Derechos
© 2022, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Publicado en
Potential Analysis, 2024, 60(1), 139-172
Editorial
Springer Nature
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Palabras clave
Determinantal point processes
Fekete points
Gegenbauer polynomials
Point distributions
Resumen/Abstract
In this paper we compute the logarithmic energy of points in the unit interval [-1,1] chosen from different Gegenbauer Determinantal Point Processes. We check that all the different families of Gegenbauer polynomials yield the same asymptotic result to third order, we compute exactly the value for Chebyshev polynomials and we give a closed expression for the minimal possible logarithmic energy. The comparison suggests that DPPs cannot match the value of the minimum beyond the third asymptotic term.
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© 2022, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.Excepto si se señala otra cosa, la licencia del ítem se describe como © 2022, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.