Abstract
We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.
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Bourget, A., Jakobson, D., Min-Oo, M. et al. A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials. Letters in Mathematical Physics 64, 105–118 (2003). https://doi.org/10.1023/A:1025764002987
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DOI: https://doi.org/10.1023/A:1025764002987