Löwner equations and dispersionless hierarchies
Takashi Takebe, Lee-Peng Teo, Anton Zabrodin
Abstract
Using the Hirota representation of dispersionless dKP and dToda hierarchies, we show that the chordal Löwner equations and radial Löwner equations respectively serve as consistency conditions for one variable reductions of these integrable hierarchies. We also clarify the geometric meaning of this result by relating it to the eigenvalue distribution of normal random matrices in the large N limit.
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