### 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 |
---|---|

Journal | Electronic Communications in Probability |

Volume | 3 |

Publication status | Published - Nov 17 1998 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Electronic Communications in Probability*,

*3*.

**Wiener soccer and its generalization.** / Baryshnikov, Yuliy.

Research output: Contribution to journal › Article

*Electronic Communications in Probability*, vol. 3.

}

TY - JOUR

T1 - Wiener soccer and its generalization

AU - Baryshnikov, Yuliy

PY - 1998/11/17

Y1 - 1998/11/17

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3042789515&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042789515&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3042789515

VL - 3

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

ER -