Studying the behaviour of the replicator coalescent considering migration.

Studying the behaviour of the replicator coalescent considering migration.

Probability

Statistics

Jaime Grau García

2025

Andreas Kyprianou, Pedro Martín Chávez

The replicator coalescent considering migration, is a stochastic model which describes a population of \textit{k} distinct types which undergo either pairwise mergers or individual migration at rates depending on their types. It turns out that if we consider the initial population to tend to infinity and dilate the time arbitrarily close to 0, the process behaves deterministically like the solution to an M-replicator equation ODE, where M is the expected payoff matrix of the process. Furthermore, the process comes down from infinity in the sense that Kingman introduced for the 'Kingman coalescent death chains'.

Markov chain, death chain, coalescent equations, collision model