Abstracts > Sigarreta Ricardo Saylé

Second-order free probability provides a framework for studying fluctuations of large random matrices beyond their limiting spectral distributions. In this talk, we derive functional equations governing the multiplicative convolution of two second-order free random variables a and b. These relations extend classical first-order descriptions and could allow one to compute fluctuation quantities associated with products of free elements. As applications, we analyze conjugation by a free circular element and investigate connections with finite free probability.