Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a positive contraction acting on a ''doubled'' o...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211180 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures. Shinji Koshida. SIGMA 17 (2021), 008, 35 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862596936592261120 |
|---|---|
| author | Koshida, Shinji |
| author_facet | Koshida, Shinji |
| citation_txt | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures. Shinji Koshida. SIGMA 17 (2021), 008, 35 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a positive contraction acting on a ''doubled'' one-particle space with an additional structure defines a unique PfPP. Recently, Olshanski inverted the direction from free fermions to DPPs, proposed a scheme to construct a fermionic state from a quasi-invariant probability measure, and introduced the notion of perfectness of a probability measure. We propose a method to check the perfectness and show that Schur measures are perfect as long as they are quasi-invariant under the action of the symmetric group. We also study conditional measures for PfPPs associated with projection operators. Consequently, we show that the conditional measures are again PfPPs associated with projection operators onto subspaces explicitly described.
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| first_indexed | 2026-03-13T23:38:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211180 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T23:38:27Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Koshida, Shinji 2025-12-25T13:24:01Z 2021 Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures. Shinji Koshida. SIGMA 17 (2021), 008, 35 pages 1815-0659 2020 Mathematics Subject Classification: 60G55; 46L53; 46L30 arXiv:2005.02837 https://nasplib.isofts.kiev.ua/handle/123456789/211180 https://doi.org/10.3842/SIGMA.2021.008 The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a positive contraction acting on a ''doubled'' one-particle space with an additional structure defines a unique PfPP. Recently, Olshanski inverted the direction from free fermions to DPPs, proposed a scheme to construct a fermionic state from a quasi-invariant probability measure, and introduced the notion of perfectness of a probability measure. We propose a method to check the perfectness and show that Schur measures are perfect as long as they are quasi-invariant under the action of the symmetric group. We also study conditional measures for PfPPs associated with projection operators. Consequently, we show that the conditional measures are again PfPPs associated with projection operators onto subspaces explicitly described. The author is grateful to Makoto Katori, Tomoyuki Shirai, and Sho Matsumoto for discussions and comments on the manuscript. He also thanks the anonymous referees for their useful suggestions for improvements of the manuscript. This work was supported by the Grant-in-Aid for JSPS Fellows (No. 19J01279). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures Article published earlier |
| spellingShingle | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures Koshida, Shinji |
| title | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures |
| title_full | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures |
| title_fullStr | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures |
| title_full_unstemmed | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures |
| title_short | Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures |
| title_sort | pfaffian point processes from free fermion algebras: perfectness and conditional measures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211180 |
| work_keys_str_mv | AT koshidashinji pfaffianpointprocessesfromfreefermionalgebrasperfectnessandconditionalmeasures |