  This paper investigates whether in frictional granular packings, like in
Hamiltonian amorphous elastic solids, the stress autocorrelation matrix
presents long range anisotropic contributions just as elastic Green's
functions. We find that in a standard model of frictional granular packing this
is not the case. We prove quite generally that mechanical balance and material
isotropy constrain the stress auto-correlation matrix to be fully determined by
two spatially isotropic functions: the pressure and torque auto-correlations.
The pressure and torque fluctuations being respectively normal and hyperuniform
force the stress autocorrelation to decay as the elastic Green's function.
Since we find the torque fluctuations to be hyper-uniform, the culprit is the
pressure whose fluctuations decay slower than normally as a function of the
system's size. Investigating the reason for these abnormal pressure
fluctuations we discover that anomalous correlations build up already during
the compression of the dilute system before jamming. Once jammed these
correlations remain frozen. Whether this is true for frictional matter in
general or is it the consequence of the model properties is a question that
must await experimental scrutiny and possible alternative models.
