Wiener soccer and its generalization

Yuliy Baryshnikov

Research output: Contribution to journalArticle

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 languageEnglish
JournalElectronic Communications in Probability
Volume3
Publication statusPublished - Nov 17 1998
Externally publishedYes

Fingerprint

Trajectory
Asymptotic Normality
Covariance matrix
Brownian motion
Genus
Inverse Problem
Ball
Game
Generalization
Soccer
Model
Inverse problem
Asymptotic normality
Geometry

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Wiener soccer and its generalization. / Baryshnikov, Yuliy.

In: Electronic Communications in Probability, Vol. 3, 17.11.1998.

Research output: Contribution to journalArticle

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