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We consider interacting many particle systems with quenched disorder havingstrong Griffiths singularities, which are characterized by the dynamicalexponent, z, such as random quantum systems and exclusion processes. In severald=1 and d=2 dimensional problems we have calculated the inverse time-scales,t^{-1}, in finite samples of linear size, L, either exactly or numerically. Inall cases, having a discrete symmetry, the distribution function, P(t^{-1},L),is found to depend on the variable, u=t^{-1}L^{z/d}, and to be universal givenby the limit distribution of extremes of independent and identicallydistributed random numbers. This finding is explained in the framework of astrong disorder renormalization group approach when, after fast degrees offreedom are decimated out the system is transformed into a set ofnon-interacting localized excitations. The Frechet distribution of P(t^{-1},L)is expected to hold for all random systems having a strong disorder fixedpoint, in which the Griffiths singularities are dominated by disorderfluctuations.Comment: 11 pages, 11 figure

Strong Griffiths singularities in random systems and their relation to extreme value statistics