There's unlikely to be any direct link. The Levy-walk behavior is a simple consequence of geometry interacting with the distribution of particle directions that

There's unlikely to be any direct link. The Levy-walk behavior is a simple consequence of geometry interacting with the distribution of particle directions that a particle might select each time it comes off the wall. The result turns out to be scale-invariant, and was a surprise for us, as we had expected a nice integer power-law in the scaling of the gas dynamics, and it turned out to be fractional. The upshot is that when computing gas damping in high-precision force/displacement sensors, one must resort to numerical simulation. One consequence of this work, in concert with the groups at Trento and MIT is that the LIGO gravitational-wave detectors opened up their gaps between the detector masses and nearby "reaction masses". The easy gaps to open happened before Advanced LIGO turned on, and I believe that the more difficult/expensive gaps to open are being upgraded roughly now. It's fun how little table-top measurements on the minutiae of force-sensing can have impacts on whether or not we observe cataclysms billions of light-years away....