  We study the origin of the scaling behavior in frictionless granular media
above the jamming transition by analyzing their linear response. The response
to local forcing is non-self-averaging and fluctuates over a length scale that
diverges at the jamming transition. The response to global forcing becomes
increasingly non-affine near the jamming transition. This is due to the
proximity of floppy modes, the influence of which we characterize by the local
linear response. We show that the local response also governs the anomalous
scaling of elastic constants and contact number.
