Article contents
Honest bernoulli excursions
Published online by Cambridge University Press: 14 July 2016
Abstract
For simple random walk on the integers, consider the chance that the walk has traveled distance k from its start given that its first return is at time 2n. We derive a limiting approximation accurate to order 1/n. We give a combinatorial explanation for a functional equation satisfied by the limit and show this yields the functional equation of Riemann's zeta function.
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1988
Footnotes
Research supported by NSF Grant DMS 86-00235.
References
- 8
- Cited by