The Lebesgue decomposition of the free additive convolution of two probability distributions
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Publication:948937
DOI10.1007/s00440-007-0100-3zbMath1390.46059arXivmath/0603104OpenAlexW2082244434MaRDI QIDQ948937
Publication date: 16 October 2008
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0603104
Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Free probability and free operator algebras (46L54) Cluster sets, prime ends, boundary behavior (30D40)
Related Items (29)
Approximation of Free Convolutions by Free Infinitely Divisible Laws ⋮ Local stability of the free additive convolution ⋮ Regularity results for free Lévy processes ⋮ Analytic subordination for bi-free convolution ⋮ Rectangular random matrices, related convolution ⋮ Propagation of singular behavior for Gaussian perturbations of random matrices ⋮ Convergence rate for spectral distribution of addition of random matrices ⋮ Asymptotic expansions in the CLT in free probability ⋮ An inequality for the distance between densities of free convolutions ⋮ Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method ⋮ Large deviations for the largest eigenvalue of the sum of two random matrices ⋮ Regularity for free multiplicative convolution on the unit circle ⋮ A concentration inequality and a local law for the sum of two random matrices ⋮ Local single ring theorem on optimal scale ⋮ Unnamed Item ⋮ Brown measures of free circular and multiplicative Brownian motions with self-adjoint and unitary initial conditions ⋮ Airy point process via supersymmetric lifts ⋮ The arithmetic of distributions in free probability theory ⋮ On the support of the free additive convolution ⋮ Limit theorems in free probability theory. I ⋮ Local law of addition of random matrices on optimal scale ⋮ A Khintchine decomposition for free probability ⋮ Local spectral statistics of the addition of random matrices ⋮ Remarks on absolute continuity in the context of free probability and random matrices ⋮ Unbounded derivations, free dilations, and indecomposability results for II$_1$ factors ⋮ Universality of the least singular value for the sum of random matrices ⋮ Free Infinitely Divisible Approximations of n-Fold Free Convolutions ⋮ The Brown measure of the sum of a self-adjoint element and an elliptic element ⋮ Subordination for the sum of two random matrices
Cites Work
- The arithmetic of distributions in free probability theory
- Atoms and regularity for measures in a partially defined free convolution semigroup
- Addition of certain non-commuting random variables
- The analogues of entropy and of Fisher's information measure in free probability theory. I
- Composition operators and classical function theory
- Processes with free increments
- Superconvergence to the central limit and failure of the Cramér theorem for free random variables
- A note on regularity for free convolutions
- A new approach to subordination results in free probability
- Free Random Variables
- On the free convolution with a semi-circular distribution
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