Abstract
In this review paper, we demonstrate that several classes of point processes in a locally compact
Polish space $X$ appear as the joint spectral measure of a rigorously defined particle density of
a representation of the canonical anticommutation relations (CAR) or the canonical commutation
relations (CCR) in a Fock space. For these representations of the CAR/CCR, the vacuum state on
the corresponding $*$-algebra is quasi-free. The classes of point process that arise in such a
way include determinantal and permanental point processes.
Key words: Projection spectral theorem, quasi-free state, determinantal point process,
permanental point process, Poisson point process, hafnian point process.
Full Text
Article Information
| Title | The projection spectral theorem, quasi-free states and point processes |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 2, 136-152 |
| DOI | 10.31392/MFAT-npu26_2.2025.04 |
| Milestones | Received 27/08/2025; Revised 12/12/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Eugene Lytvynov
Department of Mathematics, Swansea University, Bay Campus, Swansea SA1 8EN, U.K
Citation Example
Eugene Lytvynov, The projection spectral theorem, quasi-free states and point processes, Methods Funct. Anal. Topology 31
(2025), no. 2, 136-152.
BibTex
@article {MFAT2106,
AUTHOR = {Eugene Lytvynov},
TITLE = {The projection spectral theorem, quasi-free states and point processes},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {2},
PAGES = {136-152},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_2.2025.04},
URL = {https://mfat.imath.kiev.ua/article/?id=2106},
}
