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- W2081542007 abstract "We study analytically the distribution of the minimum of a set of hierarchically correlated random variables ${E}_{1},$ ${E}_{2},dots{},$ ${E}_{N}$ where ${E}_{i}$ represents the energy of the ith path of a directed polymer on a Cayley tree. If the variables were uncorrelated, the minimum energy would have an asymptotic Gumbel distribution. We show that due to the hierarchical correlations, the forward tail of the distribution of the minimum energy becomes highly nonuniversal, depends explicitly on the distribution of the bond energies $ensuremath{epsilon},$ and is generically different from the superexponential forward tail of the Gumbel distribution. The consequence of these results to the persistence of hierarchically correlated random variables is discussed and the persistence is also shown to be generically anomalous." @default.
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- W2081542007 date "2001-09-24" @default.
- W2081542007 modified "2023-09-30" @default.
- W2081542007 title "Extreme-value statistics of hierarchically correlated variables deviation from Gumbel statistics and anomalous persistence" @default.
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- W2081542007 doi "https://doi.org/10.1103/physreve.64.046121" @default.
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