  We study the motion of a random walker in one longitudinal and d transverse
dimensions with a quenched power law correlated velocity field in the
longitudinal x-direction. The model is a modification of the Matheron-de
Marsily (MdM) model, with long-range velocity correlation. For a velocity
correlation function, dependent on transverse co-ordinates y as 1/(a+|{y_1 -
y_2}|)^alpha, we analytically calculate the two-time correlation function of
the x-coordinate. We find that the motion of the x-coordinate is a fractional
Brownian motion (fBm), with a Hurst exponent H = max [1/2, (1- alpha/4),
(1-d/4)]. From this and known properties of fBM, we calculate the disorder
averaged persistence probability of x(t) up to time t. We also find the lines
in the parameter space of d and alpha along which there is marginal behaviour.
We present results of simulations which support our analytical calculation.
