The optimal order for the p-th moment of sums of independent random variables with respect to symmetric norms and related combinatorial estimates

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65024We calculate the p-the moment of the sum of n independent random variables with respect to symmetric norm in R^n. The order of growth for upper bound p/ln p obtained in ths estimate is optimal. The result extends to generalized Lorentz spaces l_{f,w} under mild assumptions on f. Indeed, the key combinatorial estimate is obtained for the weak l_1 (l_{1,infinity})-norm. Similar results have been obtained independently by Gordon, Litvak, Schuett and Werner for Orlicz norms and by Montgomery-Smith using different techniques and avoiding the combinatorial estimate.ProbabilityOperator Algebras46B09,60G50, 60C05, 47L20The optimal order for the p-th moment of sums of independent random variables with respect to symmetric norms and related combinatorial estimatestext