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We study analytically the distribution of the minimum of a set ofhierarchically correlated random variables $E_1$, $E_2$, $...$, $E_N$ where$E_i$ represents the energy of the $i$-th path of a directed polymer on aCayley tree. If the variables were uncorrelated, the minimum energy would havean asymptotic Gumbel distribution. We show that due to the hierarchicalcorrelations, the forward tail of the distribution of the minimum energybecomes highly nnon universal, depends explicitly on the distribution of thebond energies $\epsilon$ and is generically different from thesuper-exponential forward tail of the Gumbel distribution. The consequence ofthese results to the persistence of hierarchically correlated random variablesis discussed and the persistence is also shown to be generically anomalous.Comment: 6 pages, 5 figures ep

Extreme-value statistics of hierarchically correlated variables deviation from Gumbel statistics and anomalous persistence