Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy

@article{Teodorescu2004SemiclassicalEO,
  title={Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy},
  author={Răzvan Ionuț Teodorescu and Eldad Bettelheim and Oded Agam and Anton Zabrodin and Paul B. Wiegmann},
  journal={Nuclear Physics},
  year={2004},
  volume={700},
  pages={521-532}
}

Semiclassical expansions in the Toda hierarchy and the Hermitian matrix model

An iterative algorithm for determining a type of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This type includes the solution which underlies the

Two-matrix model with semiclassical potentials and extended Whitham hierarchy

We consider the two-matrix model with potentials whose derivatives are arbitrary rational functions of fixed pole structure and the support of the spectra of the matrices are union of intervals (hard

Generic critical points of normal matrix ensembles

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian growth. It is shown that the scaling

String equations in Whitham hierarchies: τ-functions and Virasoro constraints

A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The τ-function of the corresponding solutions is obtained and the differential expressions of the

Generalized string equations for double Hurwitz numbers

Laplacian growth in a channel and Hurwitz numbers

We study the integrable structure of the 2D Laplacian growth problem with zero surface tension in an infinite channel with periodic boundary conditions in the transverse direction. Similar to the

Laplacian growth in a channel and Hurwitz numbers

We study the integrable structure of the 2D Laplacian growth problem with zero surface tension in an infinite channel with periodic boundary conditions in a transverse direction. Similarly to the

Instantons in Non-Critical Strings from the Two-Matrix Model

We derive the non-perturbative corrections to the free energy of the two-matrix model in terms of its algebraic curve. The eigenvalue instantons are associated with the vanishing cycles of the curve.

Matrix model description of Laughlin Hall states

We analyse Susskind’s proposal of applying the non-commutative Chern–Simons theory to the quantum Hall effect. We study the corresponding regularized matrix Chern–Simons theory introduced by

References

SHOWING 1-10 OF 39 REFERENCES

Normal random matrix ensemble as a growth problem

Duality of Spectral Curves Arising in Two-Matrix Models

We consider the two-matrix model with the measure given by the exponential of a sum of polynomials in two different variables. We derive a sequence of pairs of “dual” finite-size systems of ODEs for

On the Structure of Correlation Functions in the Normal Matrix Model

Abstract:We study the structure of the normal matrix model (NMM). We show that all correlation functions of the model with an axially symmetric potential can be expressed in terms of a single

On the structure of Normal Matrix Model

We study the structure of the normal matrix model (NMM). We show that all correlation functions of the model with axially symmetric potentials can be expressed in terms of holomorphic functions of

2D gravity and random matrices

Laplacian growth and Whitham equations of soliton theory

Integrable structure of interface dynamics

It is established that the equivalence of 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation underlies 2D quantum gravity.

The isomonodromy approach to matric models in 2D quantum gravity

AbstractWe consider the double-scaling limit in the hermitian matrix model for 2D quantum gravity associated with the measure exp $$\sum\limits_{j = 1}^N {t_{j^{Z^{2j,} } } N \geqq 3} $$ . We show