  The change of resonance widths in an open system under a perturbation of its
interior has been recently introduced by Fyodorov and Savin [Phys. Rev. Lett.
108, 184101 (2012)] as a sensitive indicator of the nonorthogonality of
resonance states. We experimentally study universal statistics of this quantity
in weakly open two-dimensional microwave cavities and reverberation chambers
realizing scalar and electromagnetic vector fields, respectively. We consider
global as well as local perturbations, and also extend the theory to treat the
latter case. The influence of the perturbation type on the width shift
distribution is more pronounced for many-channel systems. We compare the theory
to experimental results for one and two attached antennas and to numerical
simulations with higher channel numbers, observing a good agreement in all
cases.
