Mathematical Digest Short Summaries of Articles about Mathematics in the Popular Press "Where drunkards hang out," by Ian Stewart. Nature, 18 October 2001, pages 686687. 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 239270 (2001)) has now settled the ErdosTaylor conjecture. The paper also proves an analagous result for brownian motion, which can be thought of as a continuous, nondiscrete version of a random walk.  Allyn Jackson
