| We obtain lower bounds for the measure of the ordinates where the modulus of the Riemann Zeta-function decreases as a function of its abscissa in a rectangle of size T with sides parallel to the axes.; The number-theoretic problem is reduced to a problem on random walks by means of a multidimensional analogue of the Erdos-Turan Inequality.; In dealing with the probabilistic reduction, we obtain a lower bound for the probability that a random walk with steps decreasing in size stays positive at each consecutive step. This is done using techniques from Brownian motion and Martingale Theory. |
