  The current-current correlation function is a useful concept in the theory of
electron transport in homogeneous solids. The finite-temperature conductivity
tensor as well as Anderson's localization length can be computed entirely from
this correlation function. Based on the critical behavior of these two physical
quantities near the plateau-insulator or plateau-plateau transitions in the
integer quantum Hall effect, we derive an asymptotic formula for the
current-current correlation function, which enables us to make several
theoretical predictions about its generic behavior. For the disordered
Hofstadter model, we employ numerical simulations to map the current-current
correlation function, obtain its asymptotic form near a critical point and
confirm the theoretical predictions.
