On Gegenbauer Point Processes on the Unit Interval
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 C...
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| Veröffentlicht in: | Potential analysis 2024, Vol.60 (1), p.139-172 |
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| creator | Beltrán, Carlos Delgado, Antonia Fernández, Lidia Sánchez-Lara, Joaquín |
| description | 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. |
| doi_str_mv | 10.1007/s11118-022-10045-6 |
| format | Article |
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| subjects | Asymptotic properties Chebyshev approximation Functional Analysis Geometry Logarithms Mathematics Mathematics and Statistics Polynomials Potential Theory Probability Theory and Stochastic Processes |
| title | On Gegenbauer Point Processes on the Unit Interval |
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