  We investigate the origin of the resistance fluctuations of mesoscopic
samples, near transitions between Quantum Hall plateaus. These fluctuations
have been recently observed experimentally by E. Peled et al. [Phys. Rev. Lett.
90, 246802 (2003); ibid 90, 236802 (2003); Phys. Rev. B 69, R241305 (2004)]. We
perform realistic first-principles simulations using a six-terminal geometry
and sample sizes similar to those of real devices, to model the actual
experiment. We present the theory and implementation of these simulations,
which are based on the linear response theory for non-interacting electrons.
The Hall and longitudinal resistances extracted from the Landauer formula
exhibit all the observed experimental features. We give a unified explanation
for the three regimes with distinct types of fluctuations observed
experimentally, based on a simple generalization of the Landauer-Buttiker
model. The transport is shown to be determined by the interplay between
tunneling and chiral currents. We identify the central part of the transition,
at intermediate filling factors, as the critical region where the localization
length is larger than the sample size.
