Limit theorems for radial random walks on p × q-matrices as p tends to infinity

DOI10.1002/mana.200710235zbMath1211.60001arXivmath/0703520OpenAlexW1997251584MaRDI QIDQ3074994

Michael Voit, Margit Rösler

Publication date: 10 February 2011

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703520

zbMATH Keywords

asymptoticslarge deviationsradial random walksmatrix conesBessel functions of matrix argumentBessel functions associated with root systemsBessel hypergroupslaws of large numbres

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Measures on groups and semigroups, etc. (43A05) Harmonic analysis on hypergroups (43A62) Laplace transform (44A10) Convergence of probability measures (60B10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Hypergeometric functions associated with root systems (33C67)

Related Items (5)

Bessel convolutions on matrix cones: Algebraic properties and random walks ⋮ LIMIT THEOREMS FOR RADIAL RANDOM WALKS ON EUCLIDEAN SPACES OF HIGH DIMENSIONS ⋮ Central limit theorems for multivariate Bessel processes in the freezing regime ⋮ Limit theorems for multivariate Bessel processes in the freezing regime ⋮ Integral representation and uniform limits for some Heckman-Opdam hypergeometric functions of type \textsl{BC}

Cites Work

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• Limit theorems for compact two-point homogeneous spaces of large dimensions
• Bessel functions of matrix argument
• Bessel functions associated with representations of formally real Jordan algebras
• Dependence of the Berry-Esseen estimate on the dimension
• Spaces with an abstract convolution of measures
• A limit theorem for isotropic random walks on \(R^d\) as \(d\to \infty\)
• A recursion and a combinatorial formula for Jack polynomials
• Some combinatorial properties of Jack symmetric functions
• Nonsymmetric Jack polynomials and integral kernels
• Random walks with spherical symmetry
• Special Functions of Matrix Argument. I: Algebraic Induction, Zonal Polynomials, and Hypergeometric Functions
• Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials
• A positive radial product formula for the Dunkl kernel
• Analytic Inequalities

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