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We employ the random matrix theory (RMT) framework to revisit thedistribution of resonance widths in quantum chaotic systems weakly coupled tothe continuum via a finite number M of open channels. In contrast to thestandard first-order perturbation theory treatment we do not a priory assumethe resonance widths being small compared to the mean level spacing. We showthat to the leading order in weak coupling the perturbative $\chi^2_M$distribution of the resonance widths (in particular, the Porter-Thomasdistribution at M=1) should be corrected by a factor related to a certainaverage of the ratio of square roots of the characteristic polynomial("spectral determinant") of the underlying RMT Hamiltonian. A simplesingle-channel expression is obtained that properly approximates the widthdistribution also at large resonance overlap, where the Porter-Thomas result isno longer applicable.

Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas