The Schwarz function and the shrinking of the Szegő curve: electrostatic, hydrodynamic, and random matrix models

Gabriel Álvarez, Luis Martínez Alonso, Elena Medina

We study the deformation of the classical Szegő curve ${\gamma }_0$ given by ${\gamma }_t=\{z\in \mathbb{C}:|z{e}^{1-z}|=e^{-t},|z|\le 1\}$, $t\ge 0$ from three different viewpoints: an e…