We investigate the eigenvalues of a random Schrödinger operator of Anderson type, given by \(-\Delta_g + V_\omega\), on compact manifolds with complex-valued potential. We show that, with high probability, the eigenvalues can be bounded in terms of the \(L^q\)-norm of the potential for all \(q\ge 1\). Through the use of randomization techniques, we obtain improved bounds that surpass the sharp deterministic estimates established by Sogge. This advancement draws on ideas introduced by Bourgain in the context of almost-sure scattering for lattice Schrödinger operators. This is joint work with Jean-Claude Cuenin and Konstantin Merz.
Random Schrödinger operators on compact manifolds
05.03.2026 13:30 - 14:30
Organiser:
M. Maliborski, J. Weber
Location:
BZ 9, 9. OG, OMP1
Verwandte Dateien
- Invitation 132 KB