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Largest eigenvalue distribution in the double scaling limit of matrix models: A Coulomb fluid approach

Yang Chen·Kasper J. Eriksen·Craig A. Tracy
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Abstract

Using thermodynamic arguments we find that the probability that there are no eigenvalues in the interval (-s,\infty) in the double scaling limit of Hermitean matrix models is O(exp(-s^{2m+1})) as s\to+\infty.Here m=1,2,3.. determine the m^{th} multi-critical point of the level density:σ(x)\sim b[1-(x/b)^2]^{m-1/2} and b^2\sim N.Furthermore,the size of the transition zone where the eigenvalue density becomes vanishingly small at the tail of the spectrum is \sim N^{(m-3/2)/(2m+1)} in agreement with earlier work based on the string equation.

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Yang Chen, Kasper J. Eriksen, Craig A. Tracy. 1995-02-20. Largest eigenvalue distribution in the double scaling limit of matrix models: A Coulomb fluid approach. https://doi.org/10.1088/0022-3727%2F28%2F1%2F029

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