Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications

Fabrice Gamboa (1) , Thierry Klein (1) , Clémentine Prieur (1, 2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 MOISE - Modelling, Observations, Identification for Environmental Sciences

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

Mots clés: Large and moderate deviation principles; Conditional distribution; Combinatoric problems

Domaines: Probabilités [math.PR]

Fabrice Gamboa, Thierry Klein, Clémentine Prieur. Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications. Bernoulli, 2012, 18 (4), pp.1341-1360. ⟨10.3150/11-BEJ376⟩. ⟨hal-00161003⟩