BKP hierarchy and Pfaffian point process
Mathematical Physics
2019-02-20 v2 math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1807.02259,
title = {BKP hierarchy and Pfaffian point process},
author = {Zhi-Lan Wang and Shi-Hao Li},
journal= {arXiv preprint arXiv:1807.02259},
year = {2019}
}
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17 pages