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A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials |
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| Authors: | Bourget Alain Jakobson Dmitry Min-Oo Maung Toth John A. |
| Affiliation: | (1) Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada, L8S 4K1;(2) Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Str. West, Montreal, Quebec, Canada, H3A 2K6 |
| 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. |
| Keywords: | distribution of zeros Heine– Stieltjes polynomials Lamé equation thermodynamical limit |
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