The paper provides an estimate of the total variation distance between distributions of polynomials defined on a space equipped with a logarithmically concave measure in terms of the $L^2$-distance between these polynomials.
Free Convolution of Measures via Roots of Polynomials
Distributions that arise as derivatives of families of measures
Symmetric representations of distributions over $\mathbb{R}^2$ by distributions with not more than three-point supports
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