Near-Perfect Correlation of the Resistance Components of Mesoscopic Samples at the Quantum Hall Regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the $\nu =2$ and the $\nu =1$ quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.