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Mathematics > Quantum Algebra

arXiv:0707.0425 (math)
[Submitted on 3 Jul 2007]

Title:Random Normal Matrices and Polynomial Curves

Authors:Peter Elbau
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Abstract: We show that in the large matrix limit, the eigenvalues of the normal matrix model for matrices with spectrum inside a compact domain with a special class of potentials homogeneously fill the interior of a polynomial curve uniquely defined by the area of its interior domain and its exterior harmonic moments which are all given as parameters of the potential.
Then we consider the orthogonal polynomials corresponding to this matrix model and show that, under certain assumptions, the density of the zeros of the highest relevant orthogonal polynomial in the large matrix limit is (up to some constant factor) given by the discontinuity of the Schwarz function of this polynomial curve.
Comments: 37 pages
Subjects: Quantum Algebra (math.QA); Probability (math.PR)
MSC classes: 15A52
Cite as: arXiv:0707.0425 [math.QA]
  (or arXiv:0707.0425v1 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.0707.0425

Submission history

From: Peter Elbau [view email]
[v1] Tue, 3 Jul 2007 14:33:08 UTC (38 KB)
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