We investigate the fluctuations around the mean of the Stieltjes transform of the empirical spectral distribution of any selfadjoint noncommutative polynomial in a Wigner matrix and a deterministic diagonal matrix. We obtain the convergence in distri
bution to a centred complex Gaussian process whose covariance is expressed in terms of operator-valued subordination functions.
In this article, we develop a framework to study the large deviation principle for matrix models and their quantiz
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 determi
ne the possible eigenvalues of an arbitrary polynomial $p(X_{1},X_{2})$ in case $mathcal{B}=mathbb{C}$.
