- Title
- Random walks in the plane.
- Creator
- Borwein, Jonathan M.; Nuyens, Dirk; Straub, Armin; Wan, James
- Relation
- 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'10). Proceedings of the 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'10) (San Francisco, CA 2-6 August, 2010) p. 73-82
- Relation
- http://math.sfsu.edu/fpsac/proceedings.php
- Publisher
- Discrete Mathematics and Theoretical Computer Science (DMTCS)
- Resource Type
- conference paper
- Date
- 2010
- Description
- 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 combinatorical features exhibited by the even moments which, for instance, lead to analytic continuations of the underlying integral.
- Subject
- random walks; hypergeometric functions; high-dimensional integration; analytic continuation
- Identifier
- http://hdl.handle.net/1959.13/1058094
- Identifier
- uon:16327
- Language
- eng
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