When

Start: 02/08/2012 - 1:15pm

End : 02/08/2012 - 2:15pm

End : 02/08/2012 - 2:15pm

Category

Applied Math Seminar

Speaker

Nicholas Pippenger, HMC

Abstract

We consider the classical "drunkard's walk" as a polygonal path of n steps in the plane, in which each side has unit length and the angles between successive sides are independent random variables uniformly distributed on the circle. How may self-intersections does such a walk have? We show that the mean number of self-intersections is , and that the variance is (which implies that the distribution is concentrated around its mean). We also obtain analogous results for closed polygons (walks conditioned to return to their origin after n steps), and discuss its possible extensions to other models.

This work was done jointly with Max Kutler and Maggie Rogers (both HMC Math '11).

Where

RN 103