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

Fabrice Gamboa 1 Thierry Klein 1 Clémentine Prieur 1, 2
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : 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.
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Fabrice Gamboa, Thierry Klein, Clémentine Prieur. Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2012, 18 (4), pp.1341-1360. ⟨10.3150/11-BEJ376⟩. ⟨hal-00161003⟩

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