Author:
Torre Víctor de la,Marzo Jordi
Abstract
AbstractIn 2011, Armentano, Beltrán and Shub obtained a closed expression for the expected logarithmic energy of the random point process on the sphere given by the roots of random elliptic polynomials. We consider a different approach which allows us to extend the study to the Riesz energies and to compute the expected separation distance.
Publisher
Springer Science and Business Media LLC
Reference45 articles.
1. Alishashi, K., Zamani, M.S.: The spherical ensemble and uniform distribution of points on the sphere. Electron. J. Probab. 20(23), 27 (2015)
2. Anderson, A., Dostert, M., Grabner, P.J., Matzke, R.W., Stepaniuk, T.A.: Riesz and Green energy on projective spaces. Trans. Am. Math. Soc. Ser. B 10, 1039–1076 (2023)
3. Armentano, D., Beltrán, C., Shub, M.: Minimizing the discrete logarithmic energy on the sphere: the role of random polynomials. Trans. Am. Math. Soc. 363(6), 2955–2965 (2011)
4. Beltrán, C., Delgado, A., Fernández, L., Sánchez-Lara, J.: On Gegenbauer point processes on the unit interval. Potential Anal. 60, 139–172 (2022)
5. Beltrán, C., Etayo, U.: The projective ensemble and distribution of points in odd-dimensional spheres. Constr. Approx. 48(1), 163–182 (2018)