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

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Using thermodynamic arguments we find that the probability that there are no eigenvalues in the interval (-s,∞) in the double scaling limit of Hermitean matrix models is O(exp(-s²ᵐ⁺¹)) as s→+∞.Here m=1,2,3.. determine the mth multi-critical point of the level density:σ(x) b[1-(x/b)²]ᵐ⁻¹/² and b² N.Furthermore,the size of the transition zone where the eigenvalue density becomes vanishingly small at the tail of the spectrum is N⁽ᵐ⁻³/²⁾/⁽²ᵐ⁺¹⁾ in agreement with earlier work based on the string equation.