Central Limit Theorems for Uniform Model Random Polygons

John Pardon

doi:10.1007/s10959-010-0335-2

Central Limit Theorems for Uniform Model Random Polygons

John Pardon

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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 language	English (US)
Pages (from-to)	823-833
Number of pages	11
Journal	Journal of Theoretical Probability
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s10959-010-0335-2
State	Published - Sep 2012

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

Keywords

Central limit theorem
Random polygons

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10.1007/s10959-010-0335-2

Cite this

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AB - 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 → ∞.

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KW - Random polygons

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JF - Journal of Theoretical Probability

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Central Limit Theorems for Uniform Model Random Polygons

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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