BKP hierarchy and Pfaffian point process

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.

arXiv comment17 pages

References in corpus (10)

• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Correlation functions for symmetrized increasing subsequences
• Free fermions and tau-functions
• Relating the Bures measure to the Cauchy two-matrix model
• A Limit Theorem for Shifted Schur Measures
• Application of Random Matrix Theory to Multivariate Statistics
• Pfaffian and determinantal tau functions I
• Pfaffian structures and certain solutions to BKP hierarchies I. Sums over partitions
• BKP plane partitions
• Pfaffian structures and certain solutions to BKP hierarchies II. Multiple integrals

Cited by in corpus (5)

• Bilinear equations in Darboux transformations by Boson-Fermion correspondence
• Interacting diffusions on positive definite matrices
• BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions
• Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
• Rank shift conditions and reductions of 2d-Toda theory