### 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 |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Electronic Communications in Probability |

Volume | 3 |

Publication status | Published - Nov 17 1997 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Baryshnikov, Y. (1997). Wiener soccer and its generalization.

*Electronic Communications in Probability*,*3*, 1-11.