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5. Determinantal point processes


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      Problem 5.1.

      [Carlos Beltrán] Prove optimality of the harmonic ensemble (= using the reproducing kernel of spherical harmonics) among all determinantal point processes for the Riesz energy.

      Beltrán-Marzo-Ortega-Cerdà [MR3550366] establish this for the Riesz 2-energy.


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          Problem 5.2.

          [Carlos Beltrán] Estimate from below the gap between the minimal value of the logarithmic energy and the expected logarithmic energies of determinantal point processes.


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              Problem 5.3.

              [Carlos Beltrán] Compute discrepancy/energy/separation/etc for other popular symmetric manifolds:
              1. SO(n), U(n), SU(n);
              2. Grassmannian manifolds
              3. real projective spaces
                1. Remark. See the recent preprint by Anderson et al: [arXiv:2204.04015].


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                      Problem 5.4.

                      [Thomas Leblé] Find a determinantal point process on the line, minimizing the logarithmic energy.

                          Cite this as: AimPL: Minimal energy problems with Riesz potentials, available at http://aimpl.org/energyrieszV.