Central Limit Theorem for tensor products of free variables
Abstract We establish a Central Limit Theorem for tensor product random variables $c_k:=a_k \otimes a_k$ , where $(a_k)_{k \in \mathbb {N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the semi-circle. Otherwise, the limiting law depends on the mean and variance of the variables $a_k$ and corresponds to a free interpolation between the semi-circle law and the classical convolution of two semi-circle laws.
Authors
- Cécilia Lancien (ORCID: https://orcid.org/0000-0003-2702-7775)
- Patrick Oliveira Santos (ORCID: https://orcid.org/0000-0001-7139-5538)
- Pierre Youssef (ORCID: https://orcid.org/0000-0002-1060-2342)
Institutions
- New York University Abu Dhabi (AE)
- Centre National de la Recherche Scientifique (FR)
- Université Paris-Est Créteil (FR)
- Laboratoire d’Analyse et de Mathématiques Appliquées (FR)
- Université Gustave Eiffel (FR)
- Institut Fourier (FR)
- Institut des langues et cultures d'Europe, Amérique, Afrique, Asie et Australie (FR)
- Université Grenoble Alpes (FR)
Publication Details
- Journal
- Canadian Journal of Mathematics
- Published
- 2024-12-16
- DOI
- https://doi.org/10.4153/s0008414x24001147
- Citations
- 2
- Primary Topic
- Probability and Risk Models
- Type
- article
- Field-Weighted Citation Impact
- 0.98
Funders
- New York University Abu Dhabi
- Agence Nationale de la Recherche
- Université Gustave Eiffel