Analogues of Poisson Type Limit Theorems in Discrete BM-Fock Spaces

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-10-22 DOI:10.1142/s0219025723500170

Lahcen Oussi, Janusz Wysocza'nski

引用次数: 1

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.

查看原文本刊更多论文

离散BM-Fock空间中泊松极限定理的类似项

我们给出了与若干正对称锥相关的非交换bm无关的泊松极限分布的类似情形。构造了具有创造、湮灭和守恒算子的相关离散Fock空间，并证明了它们的泊松极限定理。正锥的性质，特别是它们所具有的体积特性，以及标记的非交叉分区的组合，在这些考虑中起着至关重要的作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.