Genus-zero Whitham hierarchies in conformal-map dynamics

Abstract

A scheme for solving quasiclassical string equations is developped to prove that genus-zero Whitham hierarchies describe the deformations of planar domains determined by rational conformal maps. This property is applied in normal matrix models to show that deformations of simply-connected supports of eigenvalues under changes of coupling constants are governed by genus-zero Whitham hierarchies.

12 pages, 3 figures

References in corpus (2)

• Normal random matrix ensemble as a growth problem
• Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy

Cited by in corpus (1)

• Semiclassical expansions in the Toda hierarchy and the hermitian matrix model