A quantum central limit theorem for sums of IID random variables

Vojkan Jaksic (1) , Yan Pautrat (2) , Claude-Alain Pillet (3, 4, 5)

1 Department of Mathematics and Statistics [Montréal]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 CPT - Centre de Physique Théorique - UMR 6207
4 CPT - Centre de Physique Théorique - UMR 7332
5 CPT - E5 Physique statistique et systèmes complexes

We formulate and prove a general central limit theorem for sums of independent identically distributed non-commutative random variables.

Mots clés: Quantum probability; central limit theorem; Levy-Cramer

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]; Physique mathématique [math-ph]

Vojkan Jaksic, Yan Pautrat, Claude-Alain Pillet. A quantum central limit theorem for sums of IID random variables. Journal of Mathematical Physics, 2010, 51 (1), pp.015208. ⟨10.1063/1.3285287⟩. ⟨hal-00423440⟩