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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