arminstraub.com

# Random walks in the plane

Random walks in the plane
Jonathan M. Borwein, Dirk Nuyens, Armin Straub, James WanDiscrete Mathematics and Theoretical Computer Science — Special volume for FPSAC 2010 — 2010, Pages 191-202

## Abstract

We study the expected distance of a two-dimensional walk in the plane with unit steps in random directions. A series evaluation and recursions are obtained making it possible to explicitly formulate this distance for small number of steps. Formulae for all the moments of a $$2$$-step and a $$3$$-step walk are given, and an expression is conjectured for the $$4$$-step walk. The paper makes use of the combinatorial features exhibited by the even moments which, for instance, lead to analytic continuations of the underlying integral.

http://dmtcs.episciences.org/2862

@article{walks-fpsac-2010,
}