Analogues of Poisson type limit theorems in discrete bm-Fock spaces
Combinatorics
2023-10-10 v3
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.
Keywords
Cite
@article{arxiv.2210.12559,
title = {Analogues of Poisson type limit theorems in discrete bm-Fock spaces},
author = {Lahcen Oussi and Janusz Wysoczański},
journal= {arXiv preprint arXiv:2210.12559},
year = {2023}
}