E. Sparre-Andersen and the combinatorial method for coin-tossing

Henry P. McKean, Courant Institute, NYU

This talk is about the discovery by Sparre- Andersen that changes of sign in coin-tossing and more general games of chance is a purely combinatorial business, having nothing to do with the distribution of a single toss provided only that gain or loss be equally likely. It can be discussed via the permutation group (this is the combinatorial aspect), convolution algebra with projection, Wiener-Hopf, Feynman-Kac, etc.