We study the quantum Hall transition using the density–density correlation function. We show that in the limit ℏ → 0 the electron density moves along the percolating trajectories, undergoing normal diffusion. The localization exponent coincides with its percolation value ν=4/3. The framework provides a natural way to study the renormalization group flow from percolation to quantum Hall transition. We also confirm numerically that the critical conductivity of a classical limit of quantum Hall transition is [Formula: see text].