Analogues of Poisson type limit theorems in discrete bm-Fock spaces

TL;DR

This paper develops Poisson limit theorems within discrete bm-Fock spaces linked to positive symmetric cones, utilizing combinatorics and cone properties to extend noncommutative probability theory.

Contribution

It introduces analogues of Poisson limit theorems for noncommutative bm-independence in discrete Fock spaces associated with symmetric cones.

Findings

Established Poisson type limit theorems for noncommutative bm-Fock spaces.

Demonstrated the role of cone properties and noncrossing partitions in these theorems.

Constructed discrete Fock spaces with creation, annihilation, and conservation operators.

Abstract

We present analogues of the Poisson limit distribution for the noncommutative bm-independence, which is associated with several positive symmetric cones. We construct related discrete Fock spaces with creation, annihilation and conservation operators, and prove Poisson type limit theorems for them. Properties of the positive cones, in particular the volume characteristic property they enjoy, and the combinatorics of labelled noncrossing partitions, play crucial role in these considerations.