  Population protocols have been introduced as a model of sensor networks
consisting of very limited mobile agents with no control over their own
movement. A population protocol corresponds to a collection of anonymous
agents, modeled by finite automata, that interact with one another to carry out
computations, by updating their states, using some rules. Their computational
power has been investigated under several hypotheses but always when restricted
to finite size populations. In particular, predicates stably computable in the
original model have been characterized as those definable in Presburger
arithmetic. We study mathematically the convergence of population protocols
when the size of the population goes to infinity. We do so by giving general
results, that we illustrate through the example of a particular population
protocol for which we even obtain an asymptotic development. This example shows
in particular that these protocols seem to have a rather different
computational power when a huge population hypothesis is considered.
