Addendum to " Sum rules via large deviations "

Fabrice Gamboa (1) , Jan Nagel (2) , Alain Rouault (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich
3 LMV - Laboratoire de Mathématiques de Versailles

In these notes we fill a gap in a proof in Section 4 of Gamboa, Nagel, Rouault [Sum rules via large deviations, J. Funct. Anal. 270 (2016), 509-559]. We prove a general theorem which combines a LDP with a convex rate function and a LDP with a non-convex one. This result will be used to prove LDPs for spectral matrix measures and for spectral measures on the unit circle.

Mots clés: random measures; Large deviations

Domaines: Probabilités [math.PR]

Fabrice Gamboa, Jan Nagel, Alain Rouault. Addendum to " Sum rules via large deviations ". 2016. ⟨hal-01369130v1⟩