Indexing metadata

Discrepancy Convergence for the Drunkard's Walk on the Sphere


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Discrepancy Convergence for the Drunkard's Walk on the Sphere
 
2. Creator Author's name, affiliation, country Francis Edward Su; Harvey Mudd College
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) discrepancy, random walk, Gelfand pairs, homogeneous spaces, Legendre polynomials
 
3. Subject Subject classification Primary 60B15; Secondary 43A85
 
4. Description Abstract We analyze the drunkard's walk on the unit sphere with step size $\theta$ and show that the walk converges in order $C/\sin^2(\theta)$ steps in the discrepancy metric ($C$ a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2001-02-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/75
 
10. Identifier Digital Object Identifier 10.1214/EJP.v6-75
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 6
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.