Related papers: Pfaffian Interaction and $BCD$-quiver Matrix Model…
It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the…
Correlation functions for matrix ensembles with orthogonal and unitarysymplectic rotation symmetry are more complicated to calculate than in the unitary case. The supersymmetry method and the orthogonal polynomials are two techniques to…
In the past decades, determinants and Pfaffians were found for eigenvalue correlations of various random matrix ensembles. These structures simplify the average over a large number of ratios of characteristic polynomials to integrations…
The calculation of correlation functions for $\beta=1$ random matrix ensembles, which can be carried out using Pfaffians, has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size N. This same…
We study two generalizations of the Pfaffian to non-antisymmetric matrices and derive their properties and relation to each other. The first approach is based on the Wigner normal-form, applicable to conjugate-normal matrices, and retains…
The paper introduces a method of partial fractions with matrix coefficients and its applications to finding chains of generalized eigenvectors, to evaluation of matrix exponentials, and to solution of linear systems of ordinary differential…
Spanning trees are a representative example of linear matroid bases that are efficiently countable. Perfect matchings of Pfaffian bipartite graphs are a countable example of common bases of two matrices. Generalizing these two examples,…
A. Albouy and R. Moeckel in 2000 found some interesting inequalities related to the inverse problem for collinear (Moulton) central configurations: the Pfaffian of a certain matrix is positive since all coefficients of some polynomials are…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
Amitsur's formula, which expresses det(A+B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian of block matrices. As applications, in upcoming papers we…
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
We consider the monomer-dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian formula for the corresponding partition function,…
The Jacobian matrix of a dynamic system and its principal minors play a prominent role in the study of qualitative dynamics and bifurcation analysis. When interpreting the Jacobian as an adjacency matrix of an interaction graph, its…
The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial / topological argument. These functions are then extended into a larger family of…
We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of [1, 2] is used to evaluate the resulting series expansion for the partition function. We show that, for…
A class of interacting particle systems on $\mathbb{Z}$, involving instantaneously annihilating or coalescing nearest neighbour random walks, are shown to be Pfaffan point processes for all deterministic initial conditions. As diffusion…
A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.
Partition functions of two different matrix models for QCD with chemical potential are computed for an arbitrary number of quark and complex conjugate anti-quark flavors. In the large-N limit of weak nonhermiticity complete agreement is…
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…
On the basis of Chern-Simons field-theoretical description we propose a simple method for derivation of model interactions for Pfaffian paired states. We verify the method in the case of Pfaffian (i.e. Moore - Read) state, and derive a…