A Problem on Random Walk
R. Sherman Lehman · 1951
Abstract : From an urn containing an equal number of each of I kinds of balls, random drawings are made. After each drawing the ball is returned to the urn, so that each drawing is independent of every other. If the drawings are repeated indefinitely, what is the probability that after some drawing in the sequence an equal number of each of the I kinds of balls will have been drawn? This problem can be interpreted as a random walk in a network of streets in (I -1)-dimensional space. The drawing of a ball of a given kind is represented by the walker's moving a fixed distance in a given direction. Equalization is represented by a return to the origin.