Non-Archimedean integrals as limits of complex integrals

Abstract

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 nonstandard 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.