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

Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records