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

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