Spectral uncertainty principles at low energy: unique continuation when you don't expect it

We review an abstract and simple uncertainty principle from 'A. Boutet de Monvel, D. Lenz and P. Stollmann: An uncertainty principle, Wegner estimates and localization near fluctuation boundaries. Math. Z. 2010' and its application to graphs and divergence form operators with rough coefficients based on

D. Lenz, P. Stollmann and Gunter Stolz: An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs, arXiv: 1606.07476
P. Stollmann and Gunter Stolz: Lower bounds for Dirichlet Laplacians and uncertainty principles, arXiv:1808.04202