Journal of Statistical Physics, Vol. 53, Nos. 3/4, 1988. p. 977-983.
A random walker in R^N is considered. At each step the walker picks a point in R^N from a fixed finite set of destination points. Having chosen the point, the walker moves a fraction r (r<1) of the distance toward the point along a straight line. Assuming that the successive destination points are chosen independently, it is shown that the asymptotic distribution of the walker's position has the same mean as the destination point distribution. An estimate is obtained for the fraction of time the walker stays within a ball centered at the
mean value for almost every destination sequence. Examples show that the asymptotic distribution could have intricate structure.