Extreme value distributions for weakly correlated fitnesses in block model

TL;DR

This paper investigates the limit distribution of the maximum fitness in models with weakly correlated, identically distributed random variables, revealing connections to known laws and discovering new distributions under specific conditions.

Contribution

It characterizes the extreme value distributions for weakly correlated fitness models, identifying when they relate to known laws or form new distributions, and specifies the conditions for these results.

Findings

Extreme value distributions relate to known laws or parent distribution.

New limiting distributions are identified for certain parent distributions.

Conditions for the applicability of these results are established.

Abstract

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.