  We review how the renormalized force correlator Delta(u), the function
computed in the functional RG field theory, can be measured directly in
numerics and experiments on the dynamics of elastic manifolds in presence of
pinning disorder. We show how this function can be computed analytically for a
particle dragged through a 1-dimensional random-force landscape. The limit of
small velocity allows to access the critical behavior at the depinning
transition. For uncorrelated forces one finds three universality classes,
corresponding to the three extreme value statistics, Gumbel, Weibull, and
Frechet. For each class we obtain analytically the universal function Delta(u),
the corrections to the critical force, and the joint probability distribution
of avalanche sizes s and waiting times w. We find P(s)=P(w) for all three
cases. All results are checked numerically. For a Brownian force landscape,
known as the ABBM model, avalanche distributions and Delta(u) can be computed
for any velocity. For 2-dimensional disorder, we perform large-scale numerical
simulations to calculate the renormalized force correlator tensor
Delta_{ij}(u), and to extract the anisotropic scaling exponents zeta_x >
zeta_y. We also show how the Middleton theorem is violated. Our results are
relevant for the record statistics of random sequences with linear trends, as
encountered e.g. in some models of global warming. We give the joint
distribution of the time s between two successive records and their difference
in value w.
