*Title: Random Schroedinger operators with scaled Gibbsian potentials*

**Abstract:**
This talk describes the almost sure infinite volume
asymptotics of the ground state energy of
random Schroedinger operators with scaled Gibbsian potentials.
The random potential is obtained by distributing soft obstacles
according to an infinite volume grand canonical tempered Gibbs measure
with a superstable pair interaction.
There is no restriction on the strength of the pair interaction:
it may be taken, e.g., at a critical point.
The potential is scaled with the box size in a critical way,
i.e. the scale is determined by the typical size of large deviations
in the Gibbsian cloud.
The almost sure infinite volume asymptotics of the ground state energy
is described in terms of variational principles involving only
thermodynamic quantities.
Depending on the dimension and on the critical exponents of
the free energy density, some cases lead to a phase transition
of the asymptotic behaviour of the ground state energy.