93 citations · 766 across the 42 of their papers we have counts for
14 papers · 1 filter
Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
Ludovic Alarie-Vezina, Olivier Blondeau-Fournier, Patrick Desrosiers +2
We present a review of the most important results in the theory of symmetric functions in superspace (or symmetric superpolynomials), summarizing all principal contributions since…
Scaling limits of correlations of characteristic polynomials for the Gaussian beta-ensemble with external source
Patrick Desrosiers, Dang-Zheng Liu
We study the averaged product of characteristic polynomials of large random matrices in the Gaussian beta-ensemble perturbed by an external source of finite rank. We prove that at…
Macdonald polynomials in superspace as eigenfunctions of commuting operators
O. Blondeau-Fournier, P. Desrosiers, L. Lapointe +1
A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonali…
Macdonald polynomials in superspace: conjectural definition and positivity conjectures
O. Blondeau-Fournier, P. Desrosiers, L. Lapointe +1
We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity rela…
Asymptotics for products of characteristic polynomials in classical -Ensembles
Patrick Desrosiers, Dang-Zheng Liu
We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi -ensembles of random matrices. More specifically, we calculate…
Selberg Integrals, Super hypergeometric functions and Applications to -Ensembles of Random Matrices
Patrick Desrosiers, Dang-Zheng Liu
We study a new Selberg-type integral with indeterminates, which turns out to be related to the deformed Calogero-Sutherland systems. We show that the integral satisfies a hol…
Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
Patrick Desrosiers, Luc Lapointe, Pierre Mathieu
The Jack polynomials P_λ^{(α)} at α=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N va…
Supermatrix models, loop equations, and duality
Patrick Desrosiers, Bertrand Eynard
We study integrals over Hermitian supermatrices of arbitrary size , that are parametrized by an external field and a source , of respective size and . We sho…
Duality in random matrix ensembles for all Beta
Patrick Desrosiers
Gaussian and Chiral Beta-Ensembles, which generalise well known orthogonal (Beta=1), unitary (Beta=2), and symplectic (Beta=4) ensembles of random Hermitian matrices, are considere…
A note on biorthogonal ensembles
Patrick Desrosiers, Peter J. Forrester
We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These syst…
Relationships between -function and Fredholm determinant expressions for gap probabilities in random matrix theory
Patrick Desrosiers, Peter J. Forrester
The gap probabilities at the hard and soft edges of scaled random matrix ensembles with orthogonal symmetry are known in terms of -functions. Extending recent work relating to t…
Asymptotic correlations for Gaussian and Wishart matrices with external source
Patrick Desrosiers, Peter J. Forrester
We consider ensembles of Gaussian (Hermite) and Wishart (Laguerre) hermitian matrices. We study the effect of finite rank perturbations of these ensembles by a source t…
Orthogonality of Jack polynomials in superspace
Patrick Desrosiers, Luc Lapointe, Pierre Mathieu
Jack polynomials in superspace, orthogonal with respect to a ``combinatorial'' scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace,…
Hermite and Laguerre -ensembles: asymptotic corrections to the eigenvalue density
Patrick Desrosiers, Peter J. Forrester
We consider Hermite and Laguerre -ensembles of large random matrices. For all even, corrections to the limiting global density are obtained, and the limiting den…