L\"owner equations and dispersionless hierarchies
Complex Variables
2009-11-11 v1 Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
Using the Hirota representation of dispersionless dKP and dToda hierarchies, we show that the chordal L\"owner equations and radial L\"owner 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.
Cite
@article{arxiv.math/0605161,
title = {L\"owner equations and dispersionless hierarchies},
author = {Takashi Takebe and Lee-Peng Teo and Anton Zabrodin},
journal= {arXiv preprint arXiv:math/0605161},
year = {2009}
}
Comments
30 pages, 5 figures, amsart.cls, graphics.sty, psfrag.sty etc. are used