  We analyze electron-phonon correlation functions measured in 1D polaron
ground states of the Holstein Hamiltonian using the Global-Local variational
method. The spatial collapse of electron-phonon correlations is found to occur
in concert with transition behavior in other polaron properties, providing
mutually confirming evidence for a self-trapping line in 1D. The spatial extent
of electron-phonon correlations is used to quantify polaron size, and is
analyzed over a wide range of parameters. Distinct scaling behaviors are found
to be characteristic of the region below the self-trapping transition and above
it, contrary to some widely-held expectations and leading naturally to the
notion of the polaron size as an order parameter for a self-trapping transition
that becomes critical in the adiabatic limit.
