Central Limit Theorems for Uniform Model Random Polygons

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Abstract

We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have asymptotically the same expectation and variance. We use integral geometric expressions for these expectations and variances to reduce the desired estimates to the convergence (1+α/n) n→ eα as n → ∞.

Original languageEnglish (US)
Pages (from-to)823-833
Number of pages11
JournalJournal of Theoretical Probability
Volume25
Issue number3
DOIs
StatePublished - Sep 1 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Keywords

  • Central limit theorem
  • Random polygons

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