The Hermitian Two Matrix Model with an Even Quartic Potential(English, Paperback, Duits Maurice)

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The Hermitian Two Matrix Model with an Even Quartic Potential(English, Paperback, Duits Maurice) is written by Duits Maurice and published by American Mathematical Society. It's available with International Standard Book Number or ISBN identification 0821869280 (ISBN 10) and 9780821869284 (ISBN 13).

The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.