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We consider interacting many particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, $z$, such as random quantum systems and exclusion processes. In several $d=1$ and $d=2$ dimensional problems we have calculated the inverse time-scales, $tau^{-1}$, in finite samples of linear size, $L$, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, $P(tau^{-1},L)$, is found to depend on the variable, $u=tau^{-1}L^{z/d}$, and to be universal given by the limit distribution of extremes of independent and identically distributed random numbers. This finding is explained in the framework of a strong disorder renormalization group approach when, after fast degrees of freedom are decimated out the system is transformed into a set of non-interacting localized excitations.
The Fréchet distribution of $P(tau^{-1},L)$ is expected to hold for all random systems having a strong disorder fixed point, in which the Griffiths singularities are dominated by disorder fluctuations.

Research Institute for Solid State Physics and Optics, Budapest