Löwner equations and dispersionless hierarchies

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.

30 pages, 5 figures, amsart.cls, graphics.sty, psfrag.sty etc. are used

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