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BKP hierarchy and Pfaffian point process
- Publication Year :
- 2018
-
Abstract
- Inspired by Okounkov's work [\emph{Selecta Mathematica}, 7(1):57--81, 2001] which relates KP hierarchy to determinant point process, we establish a relationship between BKP hierarchy and Pfaffian point process. We prove that the correlation function of the shifted Schur measures on strict partitions can be expressed as a Pfaffian of skew symmetric matrix kernel, whose elememts are certain vacuum expectations of neutral fermions. We further show that the matrix integrals solution of BKP hierarchy can also induce a certain Pfaffian point process.<br />Comment: 17 pages
- Subjects :
- Mathematical Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1807.02259
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.nuclphysb.2018.12.028