Wiener soccer and itsgeneralization

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
Pages (from-to)1-11
Number of pages11
JournalElectronic Communications in Probability
Volume3
DOIs
Publication statusPublished - Jan 1 1998

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Wiener soccer and itsgeneralization. / Baryshnikov, Yuliy.

In: Electronic Communications in Probability, Vol. 3, 01.01.1998, p. 1-11.

Research output: Contribution to journalArticle

Baryshnikov, Yuliy. / Wiener soccer and itsgeneralization. In: Electronic Communications in Probability. 1998 ; Vol. 3. pp. 1-11.
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