  The dynamics of granular media in the jammed, glassy region is described in
terms of "modes", by applying a Principal Component Analysis (PCA) to the
covariance matrix of the position of individual grains. We first demonstrate
that this description is justified and gives sensible results in a regime of
time/densities such that a metastable state can be observed on long enough
timescale to define the reference configuration. For small enough times/system
sizes, or at high enough packing fractions, the spectral properties of the
covariance matrix reveals large, collective fluctuation modes that cannot be
explained by a Random Matrix benchmark where these correlations are discarded.
We then present a first attempt to find a link between the softest modes of the
covariance matrix during a certain "quiet" time interval and the spatial
structure of the rearrangement event that ends this quiet period. The motion
during these cracks is indeed well explained by the soft modes of the dynamics
before the crack, but the number of cracks preceded by a "quiet" period
strongly reduces when the system unjams, questioning the relevance of a
description in terms of modes close to the jamming transition, at least for
frictional grains.
