BKP hierarchy and Pfaffian point process

  title={BKP hierarchy and Pfaffian point process},
  author={Zhilan Wang and Shi-Hao Li},
  journal={Nuclear Physics B},

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)

On modified $$B$$KP systems and generalizations

We find the form of the Orlov–Schulman operator of the modified B KP hierarchy, which played a pivotal role in the construction of additional symmetries for the modified B KP hierarchy. We investigate

Rank shift conditions and reductions of 2d-Toda theory

This paper focuses on different reductions of 2-dimensional (2d-)Toda hierarchy. Symmetric and skew symmetric moment matrices are firstly considered, resulting in the differential relations between

Bilinear equations in Darboux transformations by Boson-Fermion correspondence

BKP hierarchy, affine coordinates, and a formula for connected bosonic n-point functions

We derive a formula for the connected n-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by

Interacting diffusions on positive definite matrices

We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an

Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble

This paper focuses on different reductions of the two-dimensional (2d)-Toda hierarchy. Symmetric and skew-symmetric moment matrices are first considered, resulting in differential relations between



Pfaffian and Determinantal Tau Functions

Adler, Shiota and van Moerbeke observed that a tau function of the Pfaff lattice is a square root of a tau function of the Toda lattice hierarchy of Ueno and Takasaki. In this paper, we give a

BKP plane partitions

Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h

Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials

into the algebras of skew-symmetric As and lower triangular (including the diagonal) matrices Ab (Borel matrices). We show that this splitting plays a prominent role also in the construction of the

Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs

We give simple linear algebraic proofs of the Eynard–Mehta theorem, the Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also

Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram

The first result is that the correlation functions of the Schur process are determinants with a kernel that has a nice contour integral representation in terms of the parameters of the process.

The partition function of the Bures ensemble as the τ-function of BKP and DKP hierarchies: continuous and discrete

It is shown that the time-dependent partition function of the Bures ensemble, whose measure has many interesting geometric properties, could act as the τ-function of BKP and DKP hierarchies if discrete time variables are introduced.

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This paper may be viewed as a developement of the the paper by J.van de Leur related to orthogonal and symplectic ensembles of random matrices, where the Tau functions are equal to sums over partitions and to multi-integrals.

Relating the Bures Measure to the Cauchy Two-Matrix Model

The Bures metric is a natural choice in measuring the distance of density operators representing states in quantum mechanics. In the past few years a random matrix ensemble and the corresponding

Infinite wedge and random partitions

Abstract. We use representation theory to obtain a number of exact results for random partitions. In particular, we prove a simple determinantal formula for correlation functions of what we call the