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Random Walks and Plane Arrangements in Three Dimensions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Billera, Louis J. Brown, Kenneth S. Diaconis, Persi |
| Copyright Year | 1999 |
| Abstract | The geometry of hyperplane arrangements in Euclidean space is a rich subject, which touches geometry [14], combinatorics [21], and operations research [23]. Probability was introduced into the subject by Bidigare, Hanlon, and Rockmore [2], who found a natural family of random walks associated with hyperplane arrangements. These walks were studied further by Brown and Diaconis [6]. One reason this development is exciting is that the walks admit a rather complete theory. We introduce the reader to this circle of ideas by specializing to the 3-dimensional case (planes in R). Here we are able to use tools from geometry to obtain a surprising formula for the stationary distribution of the walk. |
| Starting Page | 502 |
| Ending Page | 524 |
| Page Count | 23 |
| File Format | PDF HTM / HTML |
| DOI | 10.1080/00029890.1999.12005079 |
| Volume Number | 106 |
| Alternate Webpage(s) | http://pi.math.cornell.edu/~kbrown/papers/threedim.pdf |
| Alternate Webpage(s) | https://doi.org/10.1080/00029890.1999.12005079 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
