A conditional Berry-Esseen inequality

Thierry Klein (1) , A Lagnoux (1) , P Petit (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.

Mots clés: Berry-Esseen inequality; conditional distribution; combinatorial problems; occupancy; hashing with linear probing; random forests; branching processes; Bose-Einstein statistics

Domaines: Probabilités [math.PR]

Thierry Klein, A Lagnoux, P Petit. A conditional Berry-Esseen inequality. Journal of Applied Probability, 2019. ⟨hal-01801795v1⟩