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


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.


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    author = {Jonathan M. Borwein and Dirk Nuyens and Armin Straub and James Wan},
    title = {Random walks in the plane},
    journal = {Discrete Mathematics and Theoretical Computer Science},
    year = {2010},
    pages = {191--202},