The Hermitian two matrix model with an even quartic potential
著者
書誌事項
The Hermitian two matrix model with an even quartic potential
（Memoirs of the American Mathematical Society, no. 1022）
American Mathematical Society, 2012, c2011
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注記
"May 2012, volume 217, number 1022 (end of volume)"--T.p
Includes bibliography (p. 99-102) and index
内容説明・目次
内容説明
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.
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