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arXiv · 1903.09002

The atoms of the free additive convolution of two operator-valued distributions

Serban Belinschi·Hari Bercovici·Weihua Liu
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Abstract

Suppose that $X\_{1}$ and $X\_{2}$ are two selfadjoint random variables that are freely independent over an operator algebra $\mathcal{B}$. We describe the possible operator atoms of the distribution of $X\_{1}+X\_{2}$ and, using linearization, we determine the possible eigenvalues of an arbitrary polynomial $p(X\_{1},X\_{2})$ in case $\mathcal{B}=\mathbb{C}$.

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Serban Belinschi, Hari Bercovici, Weihua Liu. 2019-03-20. The atoms of the free additive convolution of two operator-valued distributions. https://arxiv.org/abs/1903.09002

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