On Gegenbauer Point Processes on the Unit Interval
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Show full item recordAuthor
Beltrán, Carlos; Delgado Amaro, Antonia María; Fernández Rodríguez, Lidia; Sánchez Lara, Joaquín FranciscoEditorial
Springer
Materia
Point distributions Gegenbauer polynomials Determinantal point processes Fekete points
Date
2022-10-04Referencia bibliográfica
Beltrán, C... [et al.]. On Gegenbauer Point Processes on the Unit Interval. Potential Anal (2022). [https://doi.org/10.1007/s11118-022-10045-6]
Sponsorship
CRUE-CSIC agreement; Springer NatureAbstract
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.