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Nodal Statistics for the Van Vleck Polynomials

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Abstract:

 The Van Vleck polynomials naturally arise from the generalized Lamé equation

as the polynomials of degree for which Eq. (1) has a polynomial solution of some degree k. In this paper, we compute the limiting distribution, as well as the limiting mean level spacings distribution of the zeros of any Van Vleck polynomial as N → ∞.

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, 3400 North Charles Street, 404 Krieger Hall, Baltimore, MD, 21218, USA. E-mail: abourget@math.jhu.edu, , , , , , US

    Alain Bourget

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  1. Alain Bourget
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Received: 15 February 2002 / Accepted: 7 May 2002 Published online: 14 October 2002

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Bourget, A. Nodal Statistics for the Van Vleck Polynomials. Commun. Math. Phys. 230, 503–516 (2002). https://doi.org/10.1007/s00220-002-0718-z

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  • DOI: https://doi.org/10.1007/s00220-002-0718-z

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