Wiener Soccer and Its Generalization

Yuliy Baryshnikov (University of Osnabrueck)

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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Pages: 1-11

Publication Date: November 17, 1997

DOI: 10.1214/ECP.v3-987

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