  Motivated by recent experiments on the approach to jamming of a weakly forced
granular medium using an immersed torsion oscillator [Nature 413 (2001) 407],
we propose a simple model which relates the microscopic dynamics to macroscopic
rearrangements and accounts for the following experimental facts: (1) the
control parameter is the spatial amplitude of the perturbation and not its
reduced peak acceleration; (2) a Vogel-Fulcher-Tammann-like form for the
relaxation time. The model draws a parallel between macroscopic rearrangements
in the system and extreme events whose probability of occurrence (and thus the
typical relaxation time) is estimated using extreme-value statistics. The range
of validity of this description in terms of the control parameter is discussed
as well as the existence of other regimes.
