  A study of the in-plane resistance noise on a high quality single crystal of
La_{1.97}Sr_{0.03}CuO_{4} deep inside the spin-glass phase reveals the onset of
non-Gaussianity and the insensitivity of the noise to the in-plane magnetic
field. The results indicate that the charge dynamics becomes increasingly slow
and correlated as temperature T -> 0. The analysis of the higher order noise
statistics provides evidence for the existence of a collective ground state of
charge clusters, which seem to coexist with charge-poor antiferromagnetic
domains that are frozen at such low T.
