The search of gravitational waves requires astonishingly large and sensitive detectors, with displacement sensitivity approaching the limit set by the Uncertainty Principle. The displacement fluctuations that are continuously monitored by the detectors should follow a Gaussian distribution; on the contrary up to now any gravitational wave detector shows large fluctuations that cause low probability tails superimposing to the Gaussian distribution which is followed for most of the time, thus lowering the chances for detection. This research proposal aims at understanding phenomena that might explain at least part of the low-probability, large fluctuations of the noise of gravitational wave detectors on the basis of fundamental Physics. The research will have large impact on the detection capabilities of present gravitational wave detectors, reducing the false alarm rate, and on the design of their next generations. Table-top experiments will be performed on mechanical systems that will be subjected to conditions similar to that possibly originating the low-probability, large fluctuations of the noise of gravitational wave detectors. A theoretical investigation of the phenomenon will guide the experiments and will attempt to get insight on more general results from the experimental outcome.