"Where drunkards hang out," by Ian Stewart. Nature, 18 October 2001, pages 686-687.
A random walk can be likened to the meanderings of a drunkard who is as likely to step in one direction as in any other. In 1960, the legendary mathematician Paul Erdos, together with S. James Taylor, posed a conundrum about random walks on a square lattice in the plane: How many times does the walker revisit the most frequently visited site within a given number of steps? In the article, Ian Stewart also poses the question this way: ``In other words, how many times does the drunkard go to his favorite watering hole?'' A recent paper in Acta Mathematica (186, pages 239-270 (2001)) has now settled the Erdos-Taylor conjecture. The paper also proves an analagous result for brownian motion, which can be thought of as a continuous, non-discrete version of a random walk.
--- Allyn Jackson