The Schwarz function of the shrinking Szegő curve γ_t is expressed via the Lambert W function, making the S-property equivalent to Schwarz reflection symmetry and linking electrostatic, hydrodynamic, and random matrix interpretations of Laguerre polynomial zero distributions.
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The Schwarz function and the shrinking of the Szeg\H{o} curve: electrostatic, hydrodynamic, and random matrix models
The Schwarz function of the shrinking Szegő curve γ_t is expressed via the Lambert W function, making the S-property equivalent to Schwarz reflection symmetry and linking electrostatic, hydrodynamic, and random matrix interpretations of Laguerre polynomial zero distributions.