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Journal of Statistical Mechanics: Theory and Experiment Volume 2006 July 2006 Create an alert RSS this journal

B Eynard J. Stat. Mech. (2006) P07005 doi:10.1088/1742-5468/2006/07/P07005

Universal distribution of random matrix eigenvalues near the 'birth of a cut' transition

B Eynard

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Abstract References Cited By Figures

Figure 1

Figure 1. The `birth of a cut' critical potential is such that one of the potential wells of the effective potential is just at the Fermi level. At a νth order critical point, the effective potential behaves like V_{\mathrm {eff}}(e)+ {(1/ 2\nu !)}V^{(2\nu)}_{\mathrm {eff}}(e)\, (x-e)^{2\nu }+\cdots .



Figure 2

Figure 2. The `birth of a cut' density of eigenvalues is such that one of the connected components of the support contains a very small number of eigenvalues ({\ll } n ).



Figure 3

Figure 3. Behaviour of the second derivative of the classical free energy with respect to t near the transition.



Figure 4

Figure 4. Behaviour of \epsilon_u(u-\ubar)-{1\over 2} .



Figure 5

Figure 5. Behaviour of γn.




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