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Density of Eigenvalues of Random Normal Matrices

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Abstract

The relation between random normal matrices and conformal mappings discovered by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded set. It is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve.

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References

  1. Wiegmann, P. B., Zabrodin, A.: Conformal Maps and integrable hierarchies. Commun. Math. Phys. 213(3), 523–538 (2000)

    Article  Google Scholar 

  2. Kostov, I. K., Krichever, I., Mineev-Weinstein, M., Wiegmann, P. B., Zabrodin, A.: τ-function for analytic curves. In: Random matrix models and their applications, Math. Sci. Res. Inst. Publ. 40, Cambridge: Cambridge Univ. Press, 2001, pp. 285–299

  3. Marshakov, A., Wiegmann, P., Zabrodin, A.: Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions. Commun. Math. Phys. 227(1), 131–153 (2002)

    Article  Google Scholar 

  4. Krichever, I., Marshakov, A., Zabrodin, A.: Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains. http://arxiv.org/list/hep-th/0309010, 2003

  5. Takasaki, K., Takebe, T.: Integrable Hierarchies and Dispersionless Limit. Rev. Math. Phys. 7(5), 743–808 (1995)

    Article  Google Scholar 

  6. Chau, L.-L., Zaboronsky, O.: On the Structure of Correlation Functions in the Normal Matrix Model. Commun. Math. Phys. 196(1), 203–247 (1998)

    Article  Google Scholar 

  7. Saff, E. B., Totik, V.: Logarithmic Potentials with External Fields. Grundlehren der mathematischen Wissenschaften 316, Berlin-Heidelberg-New York: Springer, 1997

  8. Johansson, K.: On Fluctuations of Eigenvalues of Random Hermitian Matrices. Duke Math J. 91, 151–204 (1998)

    Article  Google Scholar 

  9. Deift, P. A.: Orthogonal polynomials and random matrices: a Riemann-Hilbert Approach. Courant Lecture Notes in Mathematics, Vol 3, New York: Courant Institute of Mathematical Sciences, 1999

  10. Davis, P. J.: The Schwarz function and its applications. The Carus Mathematical Monographs, No. 17, Washington, DC: The Mathematical Association of America, 1974

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  1. Department of Mathematics,  , ETH-Zentrum, 8092, Zurich, Switzerland

    Peter Elbau & Giovanni Felder

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  1. Peter Elbau
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  2. Giovanni Felder
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Correspondence to Giovanni Felder.

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Communicated by L. Takhtajan

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Elbau, P., Felder, G. Density of Eigenvalues of Random Normal Matrices. Commun. Math. Phys. 259, 433–450 (2005). https://doi.org/10.1007/s00220-005-1372-z

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  • DOI: https://doi.org/10.1007/s00220-005-1372-z

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