Pólya's Random Walk Constants -- from Wolfram MathWorld
Let p(d) be the probability that a random walk on a d-D lattice returns to the origin. In 1921, Pólya proved that p(1)=p(2)=1, (1) but p(d)<1 (2) for d>2. Watson (1939), McCrea and Whipple (1940),...
mathworld.wolfram.com