Approximation of the Evolution Operator by Expectations of Functionals of Sums of Independent Random Variables

Abstract

A method of probabilistic approximation of the operator $e^{-itH}$, where $H = -\frac{1}{2}\,\frac{d^2}{dx^2}+V(x), V\in L_\infty({\mathbf{R}})$, in the strong operator topology is proposed. The approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables.