Abstract
For any integer p ≥ 1 we present a class of polynomial potentials of matrix models for which the limiting density of eigenvalues can be found explicitly in elementary functions. The support of the density consists generically from p intervals. We introduce also certain p-periodic real symmetric Jacobi matrices and we give formulas relating the limiting eigenvalue density and the potential of the considered random matrix ensembles with the density of states and the Lyapunov exponent of these Jacobi matrices.
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Buslaev, V., Pastur, L. (2002). A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures. In: Malyshev, V., Vershik, A. (eds) Asymptotic Combinatorics with Application to Mathematical Physics. NATO Science Series, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0575-3_3
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DOI: https://doi.org/10.1007/978-94-010-0575-3_3
Publisher Name: Springer, Dordrecht
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