A grain of dust falling through a Sierpinski gasket

In this paper we analyze the downward random motion of a particle in a vertical, bounded, Sierpinski gasket G, where at each layer either absorption or delays are considered. In the case of motion with absorption the explicit distribution of the position of the descending particle in the pre-gasket G(n) is obtained and the limiting case of the Sierpinski gasket discussed. For the delayed downward motion we derive a representation of the random time needed to arrive at the base of G(n) in terms of independent binomial random variables (containing the contribution of delays at different layers with different geometrical structures).