Normal-ordering approximations and translational (non)invariance

Walks, Partitions, and Normal Ordering

We describe the relation between graph decompositions into walks and the normal ordering of differential operators in the n-th Weyl algebra. Under several specifications, we study new types of restricted set partitions, and a generalization of Stirling numbers, which we call the λ-Stirling numbers.

Approximations by OBDDs and the Variable Ordering Problem

Normal approximations with Malliavin calculus

This monograph contains some recent results by the authors and their collaborators on the application of Stein’s method combined with Malliavin calculus to the normal approximation for functionals of a Gaussian process. It is addressed to researchers and graduate students in probability and statistics who would like to learn the basis of Gaussian analysis and its application to asymptotic techn...

Rook numbers and the normal ordering problem

Abstract. For an element w in the Weyl algebra generated by D and U with relation DU = UD + 1, the normally ordered form is w = ∑ ci,jU D . We demonstrate that the normal order coefficients ci,j of a word w are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients ci,j ....

Approximate substitutions and the normal ordering problem

In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations. 1. Introduction The series of papers [1, 2, 3] had two sequels. First one, algebraic, was the construction of a Hopf algebra of Feynman-Bender...