Limit theorems for compact two-point homogeneous spaces of large dimensions

DOI10.1007/BF02214654zbMath0870.60008OpenAlexW2090898661MaRDI QIDQ678081

Michael Voit

Publication date: 1 September 1997

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02214654

zbMATH Keywords

orthogonal polynomialsprojective spacescentral limit theoremshypergroupsisotropic random walks\(d\)-spheresnoncentral \(\chi^ 2\)-distribution

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (4)

Rates of convergence to Gaussian measures on \(n\)-spheres and Jacobi hypergroups ⋮ Limit theorems for random walks on the double coset spaces \(U(n)//U(n-1)\) for \(n\to \infty\) ⋮ Limit theorems for radial random walks on p × q-matrices as p tends to infinity ⋮ Asymptotics of Heat Kernels on Projective Spaces of Large Dimensions and on Disk Hypergroups

Cites Work

• One-dimensional hypergroups
• Pseudoisotropic random walks on free groups and semigroups
• Harmonic analysis of probability measures on hypergroups
• Spaces with an abstract convolution of measures
• The central limit theorem for Chébli-Trimèche hypergroups
• A central limit theorem for isotropic random walks on \(n\)-spheres for \(n\to \infty\)
• Limit theorems for random walks on the double coset spaces \(U(n)//U(n-1)\) for \(n\to \infty\)
• Positivity and the convolution structure for Jacobi series
• Banach algebras for Jacobi series and positivity of a kernel
• Two-point homogeneous spaces
• Asymptotic analysis of a random walk on a hypercube with many dimensions
• Asymptotic distributions for the Ehrenfest urn and related random walks
• Analytic Inequalities
• Random walk on spheres
• Central limit theorems for a class of polynomial hypergroups
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