Limit theorems in free probability theory. I

By Gennadiy P. Chistyakov, Friedrich Götze. 2006

87 citations recorded by the source corpus.

Based on an analytical approach to the definition of additive free convolution on probability measures on the real line, we prove free analogues of limit theorems for sums for nonidentically distributed random variables in classical probability theory.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/021b3dae2e113ae6a59bb9b07096c51ce5799ba8

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In Mathematical Physics

1. Roland Speicher
2. Moritz Weber
3. Sven Raum

In Statistics and Probability

1. Roland Speicher
2. Moritz Weber
3. Sven Raum

Citations in the corpus

• Free Probability and Random Matrices (2014, methodology): “The general case was then first treated by Bercovici and Voiculescu in [30] by operator algebraic methods; however, more recent alternative approaches, by Belinschi and Bercovici [21, 18] and by Chistyakov and Götze [53, 54], rely on the subordination formulation.”