Motion of a random walker in a quenched power law correlated velocity field.

We study the motion of a random walker in one longitudinal and transverse dimensions with a quenched power law correlated velocity field in the longitudinal direction. The model is a modification of the Matheron-de Marsily model, with long-range velocity correlation. For a velocity correlation function, dependent on transverse coordinates as , we analytically calculate the two-time correlation function of the coordinate. We find that the motion of the coordinate is a fractional Brownian motion (FBM), with a Hurst exponent . From this and known properties of FBM, we calculate the disorder averaged persistence probability of up to time . We also find the lines in the parameter space of and along which there is marginal behavior. We present results of simulations which support our analytical calculation.