On superconvergence of sums of free random variables

DOI10.1214/009117906000001132zbMath1129.46053arXivmath/0610075OpenAlexW2048125424MaRDI QIDQ2456033

Vladislav Kargin

Publication date: 17 October 2007

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

Full work available at URL: https://arxiv.org/abs/math/0610075

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Probability theory on algebraic and topological structures (60B99)

Related Items

Approximation of Free Convolutions by Free Infinitely Divisible Laws ⋮ Superconvergence in free probability limit theorems for arbitrary triangular arrays ⋮ Asymptotic expansions in the CLT in free probability ⋮ Superconvergence to freely infinitely divisible distributions ⋮ On the support of the free additive convolution ⋮ Local limit theorems in free probability theory ⋮ Estimates for compression norms and additivity violation in quantum information

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Addition of certain non-commuting random variables
• Addition of freely independent random variables
• Lévy-Hinčin type theorems for multiplicative and additive free convolution
• Stable laws and domains of attraction in free probability theory
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
• Universality at the edge of the spectrum in Wigner random matrices.
• On the distribution of the largest eigenvalue in principal components analysis
• Superconvergence to the central limit and failure of the Cramér theorem for free random variables
• On orthogonal and symplectic matrix ensembles
• The law of large numbers for free identically distributed random variables
• The central limit theorem for free additive convolution