Year: 2024
Type: article
Abstract: This work proposes algorithms for computing additive and multiplicative free convolutions of two given probability measures. We consider probability measures with compact support whose free convolution results in a probability measure with a density function that exhibits a square-root decay at the boundary (for example, the semicircle distribution or the Marchenko–Pastur distribution). A key ingredient of our method is rewriting the intermediate quantities of the free convolution using the Cauchy integral formula and then discretizing these integrals using the trapezoidal quadrature rule, which converges exponentially fast under suitable analyticity properties of the functions to be integrated.
Authors: Alice Cortinovis, Lexing Ying
Institution: Stanford University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402688131