Abstract
The trajectory of the ball in a soccer game is modelled by the Brownian motion on a cylinder, subject to elastic reflections at the boundary points (as proposed in [KPY]). The score is then the number of windings of the trajectory around the cylinder. We consider a generalization of this model to higher genus, prove asymptotic normality of the score and derive the covariance matrix. Further, we investigate the inverse problem: to what extent the underlying geometry can be reconstructed from the asymptotic score.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-11 |
| Number of pages | 11 |
| Journal | Electronic Communications in Probability |
| Volume | 3 |
| DOIs | |
| State | Published - Jan 1 1998 |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty