Asymptotics of the partition function of a Laguerre-type random matrix model

We study asymptotics of the partition function Z"N of a Laguerre-type random matrix model when the matrix order N tends to infinity. By using the Deift-Zhou steepest descent method for Riemann-Hilbert problems, we obtain an asymptotic expansion of logZ"N in powers of N^-^2.

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