English

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