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We study the arrival time distribution of overdamped particles driven by aconstant force in a piecewise linear random potential which generates thedichotomous random force. Our approach is based on the path integralrepresentation of the probability density of the arrival time. We explicitlycalculate the path integral for a special case of dichotomous disorder and usethe corresponding characteristic function to derive prominent properties of thearrival time probability density. Specifically, we establish the scalingproperties of the central moments, analyze the behavior of the probabilitydensity for short, long, and intermediate distances. In order to quantify thedeviation of the arrival time distribution from a Gaussian shape, we evaluatethe skewness and the kurtosis.

Arrival time distribution for a driven system containing quenched dichotomous disorder