A linear version of Dawson-G\"artner's theorem

TL;DR

This paper establishes a linear analogue of Dawson-Gärtner's theorem, demonstrating that weak large deviations principles and ensemble equivalence are maintained under linear projective limits.

Contribution

It introduces a linear version of Dawson-Gärtner's theorem, extending the applicability of large deviations principles to linear projective limits.

Findings

Weak large deviations principles are preserved under linear projective limits.

Ensemble equivalence remains valid through linear projective limits.

The theorem applies to vector space limits in a linear setting.

Abstract

We prove a linear version of Dawson-G\"artner's theorem saying that weak large deviations principles and the equivalence of ensembles are preserved through linear projective limits. ----- Nous d\'emontrons une version lin\'eaire du th\'eor\`eme de Dawson-G\"artner assurant que les principes de grandes d\'eviations faibles et l'\'equivalence d'ensemble sont conserv\'es par passage aux limites projectives d'espaces vectoriels.