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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 008, 35 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.008
(Mi sigma1691)
 

This article is cited in 3 scientific papers (total in 3 papers)

Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures

Shinji Koshida

Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo, Tokyo 112-8551, Japan
Full-text PDF (597 kB) Citations (3)
References:
Abstract: 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.
Keywords: Pfaffian point process, determinantal point process, CAR algebra, quasi-free state.
Funding agency Grant number
Japan Society for the Promotion of Science 19J01279
This work was supported by the Grant-in-Aid for JSPS Fellows (No. 19J01279).
Received: July 23, 2020; in final form January 16, 2021; Published online January 26, 2021
Bibliographic databases:
Document Type: Article
MSC: 60G55, 46L53, 46L30
Language: English
Citation: Shinji Koshida, “Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures”, SIGMA, 17 (2021), 008, 35 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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