The effect of a strong magnetic field on the persistent current and current-current correlations in the Laughlin geometry are discussed. Due to the violation of time-reversal symmetry a single disordered sample may carry a current even in the absence of a threading flux. Once one averages over many realizations this current disappears. A theory is presented for the current-current correlations in the presence of a strong magnetic field and compared to the results of a numerical calculation. The results fit for the bulk states while discrepancies appear for edge states.