Fast, slow convergence, and concentration in the house of cards replicator-mutator model

TL;DR

This paper analyzes the long-term behaviors of the replicator-mutator equation with house of cards mutations, providing the first concentration result and insights into convergence properties.

Contribution

It offers a detailed analysis of the model's long-term dynamics and introduces the first concentration result for this class of equations.

Findings

Identification of different convergence regimes

First concentration result for the house of cards model

Insights into slow and fast convergence behaviors

Abstract

We propose a fine analysis of the various possible long time behaviours of the solutions of the replicator-mutator equation with so-called Kingman's house of cards mutations. In particular, we give what is to our knowledge the first concentration result for this model.