  We explain how non-archimedean integrals considered by Chambert-Loir and
Ducros naturally arise in asymptotics of families of complex integrals. To
perform this analysis we work over a non-standard model of the field of complex
numbers, which is endowed at the same time with an archimedean and a
non-archimedean norm. Our main result states the existence of a natural
morphism between bicomplexes of archimedean and non-archimedean forms which is
compatible with integration.
