Percolation and lack of self-averaging in a frustrated evolutionary model

TL;DR

This paper introduces a stochastic evolutionary model that exhibits a percolation-like phase transition and non self-averaging effects, revealing complex fragmentation phenomena in evolutionary dynamics.

Contribution

It presents a new frustrated evolutionary model that extends Kauffman's rugged model and demonstrates exactly solvable phase transition and non self-averaging behavior.

Findings

Percolation-like phase transition in finite phase space

Non self-averaging effects in the thermodynamic limit

Model is exactly solvable in the thermodynamic limit

Abstract

We present a stochastic evolutionary model obtained through a perturbation of Kauffman's maximally rugged model, which is recovered as a special case. Our main results are: (i) existence of a percolation-like phase transition in the finite phase space case; (ii) existence of non self-averaging effects in the thermodynamic limit. Lack of self-averaging emerges from a fragmentation of the space of all possible evolutions, analogous to that of a geometrically broken object. Thus the model turns out to be exactly solvable in the thermodynamic limit.