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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2508.19147 |
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| _version_ | 1866912759006887936 |
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| author | Lytvynov, Eugene |
| author_facet | Lytvynov, Eugene |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The projection spectral theorem, quasi-free states and point processes Lytvynov, Eugene Mathematical Physics 46L30, 47L60, 60G55 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. |
| title | The projection spectral theorem, quasi-free states and point processes |
| topic | Mathematical Physics 46L30, 47L60, 60G55 |
| url | https://arxiv.org/abs/2508.19147 |