A functional central limit theorem for the partial sums of sorted i.i.d. random variables

Jean-François Marckert, David Renault

Let $(X_i,i\ge 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $‘E(f(X_1{)}^2)<+\infty$. We show a functional central limit theo…