%0 Journal Article %T Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators %A Denis Borisov %A Martin Tautenhahn %A Ivan Veselic %J Mathematics %D 2014 %I arXiv %X We discuss properties of $L^2$-eigenfunctions of Schr\"odinger operators and elliptic partial differential operators. The focus is set on unique continuation principles and equidistribution properties. We review recent results and announce new ones. %U http://arxiv.org/abs/1405.1659v1