  We offer a new perspective to the problem of characterizing mesoscopic
fluctuations in the inter-plateau region of the integer quantum Hall
transition. We found that longitudinal and transverse conductance fluctuations,
generated by varying the external magnetic field within a microscopic model,
are multifractal and lead to distributions of conductance increments
(magnetoconductance) with heavy tails (intermittency) and signatures of a
hierarchical structure (a cascade) in the corresponding stochastic process,
akin to Kolmogorov's theory of fluid turbulence. We confirm this picture by
interpreting the stochastic process of the conductance increments in the
framework of H-theory, which is a continuous-time stochastic approach that
incorporates the basic features of Kolmogorov's theory. The multifractal
analysis of the conductance "time series," combined with the H-theory formalism
provides, strong support for the overall characterization of mesoscopic
fluctuations in the quantum Hall transition as a multifractal stochastic
phenomenon with multiscale hierarchy, intermittency, and cascade effects.
