Rates of convergence to Gaussian measures on \(n\)-spheres and Jacobi hypergroups

DOI10.1214/aop/1024404296zbMath0873.60047OpenAlexW2017304411MaRDI QIDQ1356350

Michael Voit

Publication date: 16 October 1997

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1024404296

zbMATH Keywords

Jacobi polynomialscentral limit theoremGaussian measurestotal variation distancecompact symmetric spaces of rank onerandom walks on \(n\)-spheres

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Convergence of probability measures (60B10)

Related Items (2)

Affine Dunkl processes of type \(\widetilde{\mathrm{A}}_{1}\) ⋮ Edgeworth expansion on n-spheres and Jacobi hypergroups

Cites Work

• Limit theorems for compact two-point homogeneous spaces of large dimensions
• Convolution semigroups on hypergroups
• One-dimensional hypergroups
• Positivity of the heat kernel for ultraspherical polynomials and similar functions
• Harmonic analysis of probability measures on hypergroups
• 'Normal' distribution functions on spheres and the modified Bessel functions
• Spaces with an abstract convolution of measures
• Random rotations: Characters and random walks on \(SO(N)\)
• Hypergroup deformations and Markov chains
• Precise estimates on the rate at which certain diffusions tend to equilibrium
• The central limit theorem for Chébli-Trimèche hypergroups
• Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere
• A central limit theorem for isotropic random walks on \(n\)-spheres for \(n\to \infty\)
• The numerical solution of linear recurrence relations
• Positivity and the convolution structure for Jacobi series
• Banach algebras for Jacobi series and positivity of a kernel
• Two-point homogeneous spaces
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• Asymptotic distributions for the Ehrenfest urn and related random walks
• Random walk on spheres
• The Accuracy of the Gaussian Approximation to the Sum of Independent Variates
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