Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-09-08
J. Stat. Mech. (2011) P04020
Physics
Condensed Matter
Statistical Mechanics
Expanded, added references
Scientific paper
We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random variables drawn from a common parent distribution. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.
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