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1998 Wiener Soccer and Its Generalization
Yuliy Baryshnikov
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Electron. Commun. Probab. 3: 1-11 (1998). DOI: 10.1214/ECP.v3-987

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.

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Yuliy Baryshnikov. "Wiener Soccer and Its Generalization." Electron. Commun. Probab. 3 1 - 11, 1998. https://doi.org/10.1214/ECP.v3-987

Information

Accepted: 17 November 1997; Published: 1998
First available in Project Euclid: 2 March 2016

zbMATH: 0890.60075
MathSciNet: MR1492035
Digital Object Identifier: 10.1214/ECP.v3-987

Subjects:
Primary: 60J35
Secondary: 60J38

Keywords: Brownian motion , Wiener process

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